What is the evidence that Galerius raised Severus II to the rank of Augustus?

The basic assumption for this question rests on a very short passage in Zosimos and far reaching conclusions from that.

This answer just presupposes that Severus was indeed made augustus as correct — as also evidenced amply in ancient sources & et passim, in modern scholarship in general and in @semaphore's answer on this page in particular.

So, instead of only listing further confirmatory tidbits of evidence for the now apparently 'obvious', this post mainly tries to explain why the confusion may have arisen and that Zosimos is perhaps 'not wrong' in writing what he did.

These hints to understand the original text rest on language interpretation, translation, and 'exact chronology of events' — or rather the opposite, as this is one area of quite a bit of uncertainty: we cannot construct a 100% reliable timeline of events for these particulars, as this is not the only instance when our sources are in a bit of a disagreement or apparent contradiction to each other. Well, that is, if they are indeed for this rank issue…

That Severus was promoted to augustus seems evident. That Zosimos simply 'made an error' in his account may be possible still, but that is not assured.

One alternative 'solution' for this is that Zosimos did not exclusively mean the actual rank Severus held at the time, but instead uses this word to signify relationships of personal loyalty.

Whether this one alternative theory, supported by a more modern translation, holds up or not, the following will detail some of the problems and show a few of the possible avenues to solve this.

The original reads as:

Ταῦτα μαθὼν Μαξιμιανὸς ὁ Γαλέριος ἐκπέμπει τὸν Καίσαρα Σεβῆρον πολεμήσοντα Μαξεντίῳ.

— Zosimos, II,10 (Persues Greek text)

Which was translated as quoted without reference in the question in 1814 as identical to this version:

Maximianus Gallerius, when he had learned this, sent Severus Caesar against Maxentius with an army.

— Zosimus, New History. London: Green and Chaplin (1814). Book 2. https://www.tertullian.org/fathers/zosimus02_book2.htm

The quality of this translation is prefaced on that site with:

About this translation

This text is a copy of the 1814 English translation, which implies that it is a fresh translation with the notes of the 1679 Oxford edition. But since there is a 1684 translation which claims the same, certain points lead me to believe that it is a very careless reprint only. No translator's name or introduction is present. The printed book is littered with crass mistakes which could not have occurred had it been proof-read at all. The pagination runs up to p.125, then reverts to 124 and on. The pagination has been tampered again with between pp. 134–137 to add two to the count, so that the final number is correct. Finally the book is padded out with 70 pages of really irrelevant appendices, plainly there only to increase the price. These last have been omitted. The title page indicates that it was printed by W. Green and T. Chaplin for Mr. J. Davis, who presumably paid for this inferior product.

An original copy of this edition was not available to me in November 2002. This online text was originally prepared from a poor quality photocopy of the volume, bound as a book with the pages reversed. It has been very hard to scan. Reports of typographical errors which may have escaped me are very welcome. The copy omitted the 'second' pages 124–5 in book IV, leaving a lacuna. In August 2003 I was able to consult an original in the Taylorian Institute Annex of the Bodleian Library in Oxford, and used this to complete the edition.

Two cases where the wrong name has plainly been inserted by the compositor — Jovian for Julian, Constantine for Constantius — I have corrected. I have no doubt there are others. It has been a considerable temptation to correct the typographical errors, but I have refrained from doing so.

As usual, copying and placing copies online is encouraged.

Note that the online edition presented here has a footnote shown after the passage in question, but omits its actual content of it as 'superfluous'. While this text version of the 1814 translation was then re-used on Livius.org, that site's Jona Lendering added a note that says:

He was in fact augustus after the death of Constantius.

So, why all the confusion over what title Flavius Valerius Severus had at that moment?

Others have tried to systematise the sources around this event and highlight the incongruences as follows:

It is at once obvious that there are two quite different accounts of where Severus met his end. One places it in Ravenna in 306 and the other near Rome, probably in 307. Lactantius, who was writing probably between 318 and 321 is by far our earliest source, and, in my opinion the most reliable of the ten. Most scholars (Seeck and Moreau and many others) assume that the account of Severus' death which places it near Rome is the correct one. It is the purpose of this article to show that this opinion is not a well-founded one. We must now examine the sources in detail.

[…]

Eutropius. This author makes the error of describing Severus as Caesar when in fact he was Augustus: the author of the Excerpta Valesiana, in both his sources, makes the same error, and so do Aurelius Victor, the author of the Epitome and Zosimus. Eutropius also appears to think that it was Maxentius who pursued Severus to Ravenna. He does not introduce Maximian into the story of Severus' death at all. He is writing at some point in the middle of the fourth century.

[…]

Zosimus (second half of the fifth century): At first sight, as so often with Zosimus, the account seems detailed and convincing, but closer inspection must induce some scepticism. As far as Severus' flight to Ravenna, his narrative is convincing enough; we can overlook his description of Severus as Caesar. But it is wholly unlikely that Ravenna was, as Zosimus says, well equipped with defenders and supplies. If it was, why did Severus surrender so quickly? Zosimus reproduces the order of events whereby Maxentius chases Severus into Ravenna and Maximian then returns from retirement and visits Severus in Ravenna, an order which we have already found to be most improbable. Even more unlikely is the train of events which Zosimus' narrative next pre supposes, that Severus was persuaded to come of his own free will, not as a captive, to Rome, and was ambushed by Maxentius at Tres Tabernae on the way. It is difficult enough to conceive how Severus should have been passing through Tres Tabernae, 30 miles south of Rome, on the way from Ravenna to Rome; this can be explained (as several historians have explained it) by assuming that Zosimus is con fusing the Tres Tabernae on the Via Appia with another Tres Tabernae known to have existed on the Via Flaminia, north of Rome. What is alto gether impossible is to believe that either Maximian permitted Severus to travel unescorted as a friend as far as within a few miles of Rome, or that, had Maximian been foolish enough to expect him to do so, Severus would have been fatuous enough to follow this plan. Incidentally, Zosimus' account is not con sistent with the theory that places Severus' death in 307. We must, I believe, view Zosimus' account of the events after Severus' flight to Ravenna with grave suspicion.

It should perhaps be noted that evidence from coins or elsewhere suggesting that Severus was still recognized as Emperor in 307, or as Consul, all derives from the Eastern Empire, and only shows that Galerius and the Eastern authorities did not know of Severus' death till 307.

— R. P. C. Hanson: "The circumstances attending the death of the Emperor Flavius Valerius Severus in 306 or 307", Hermathena , Winter 1974, No. 118, (Winter 1974), pp59–68. jstor

This is perhaps because Zosimos did in fact not write exclusively about the then currently correct title for Severus — which he would have gotten 'wrong' then — but instead emphasises a part of the relationship between Galerius and Severus: ton Kaisara — his Caesar:

τὸν: ὁ lentil masc acc sg

as evidenced by this more modern English translation:

When Galerius heard this, he sent his Caesar Severus to engage Maxentius.

footnoted with:

Severus was no longer Caesar, but now Augustus, successor to Constantius. Unfortunately, his troops had served under Maximianus.

— Zosimus: "New History", A Translation with Commentary by Ronald T. Ridley, Australian Association for Byzantine Studies Byzantina Australiensia 2, ©1982 Australian Association for Byzantine Studies Department of Greek, University of Sydney, 2006.

This translation choice is certainly not the prevailing one, as a comparison with other choices reveals.

A slightly more recent translation, into Latin, reads with 'cāesărĕm accusative singular':

His cognitis, Severum caesarem Maximianus Gallerius ablegat, bellum Maxentio facturum.

— Johann Friedrich Reitemeier & Immanuel Bekker (eds, trl): "Zosimus", Impensis Ed. Weberi: Bonn, 1837. (archive.org)

The modern French translation also goes with 'the Caesar Severus':

Quand il a vent de cela, Maximien Galère envoie le César Sévère combattre Maxence ; […]

— François Paschoud (ed, trl): "Zosime. Histoire Nouvelle", Tome I, Livre I–II, Les Belles Lettres: Paris, 2000 (1971).

As does the most recent German translation:

Als Maximianus Galerius von diesen Ereignissen erfuhr, entsandte er den Caesar Severus mit dem […]

— Otto Veh & Stefan Rebenich (eds, trl): "Zosimus : Neue Geschichte / Übers. und eingel.von Otto Veh, durchges. und erl. von Stefan Rebenich", Hiersemann: Stuttgart, 1990.

But the case for Zosimos describing the relationship with an outdated by then title rather than the formal currently 'correct' title with much of his 'typical' hindsight bias in portrayals is still possible, as this kind of interpretation for Zosimos has to be considered more often:

Zosimus’ view is supported by the demonstrable instability of the imperial office, and the constant distraction of war with Persia, which prevented the development of a sustained response in Dacia and Moesia.

[…]

Zosimus adds a curious point of detail that bears this out. In his account of the later secession of Africa from Maxentius’ control, he gives the substantial reason for it as the garrison’s loyalty to Galerius. Since this is a patent error, it needs to be explained. The simplest explanation is that Zosimus or his source (presumably Eunapius) confused Galerius Valerius Maximianus with Aurelius Valerius Maximianus, that is, Galerius with Maximian. Therefore, what Zosimus is actually saying is that the African troops revolted out of loyalty to Maximian. This makes perfect sense, since the revolt occurred at a time when Maximian had been humiliated and exiled by his son.

[…]

The Origo Constantini dates Maximian’s resumption of office to the period following the defeat of Severus. This is clearly wrong since it both contradicts and makes no sense of other narratives. Zosimus, drawing upon Eunapius, tells another story. He also suggests that Maximian’s return to power was after the repulse of Severus, but all his own work, and owed nothing to an invitation from Maxentius. Following the tradition of the Kaisergeschichte, Eutropius suggests that Maximian’s coup was not inspired by Maxentius.

[…]

Early in 307, this policy was vindicated. After a conference between Galerius and Severus in Sirmium, Severus returned to Milan.116 The northern Italian diocese was still loyal, since the mints of Ticinum and Aquileia continued to strike for Galerius and Severus.117 Galerius, campaigning against the Sarmatians, could not send his own troops, so Severus was constrained to use the troops bequeathed him by Maximian. It was a gamble, although the emperors, accustomed to decades of freedom from mutiny (the last against an emperor in command had been in 281 against Probus), might not have seen it as such. If so, they miscalculated. They overestimated the loyalty of their soldiers to a previous commander. There is no doubt that the soldiers who formed Severus’ army were composed in a large part of Maximian’s veterans. Zosimus calls them “Moorish legions” – a gratuitous detail which therefore inspires some trust. Maximian had been successful in Africa, and doubtless some, or all, of these troops had served under him there. It was with this army, lately commanded by his rival, that Severus was obliged to settle the revolt of Maxentius. Lactantius notes the irony:

mittit eum cum exercitu Maximiani ad expugnandi Maximiani filium.
(he sent him with the army of Maximian to achieve the removal of Maximian’s son.)

There has been some confusion over the chronology of the conflict. Two dates are certain: April 307, when Maxentius ceased to recognize the consulships of Galerius and Daza; and 25 July, when Constantine still styled himself as a Caesar. April is the more probable month for the invasion. It sent a very clear message that Galerius had no intention of coming to terms with Maxentius. Severus’ march on Rome made the conflict unambiguous and inevitable. It was the point at which Maxentius abandoned the appearance of loyalty, took the title of Augustus and dropped the names of Galerius and Daza from his consular formulae.122 It was a bold gamble: Maxentius lacked sufficient forces to assert it. When Severus commenced his march on Rome from Milan there was no force to impede his progress. He was also able to invest the city of Rome itself. But the walls were strong and it was there that things went wrong. While it should have been easy enough to wait out a siege, the magic of Maximian’s name proved a stronger offensive tactic than Severus could withstand. His soldiers deserted and Severus was left marooned, an emperor without an army. The old commander, the old loyalty, the old fidelity, triumphed over any pretension of succession.

[…]

The implication of Zosimus’ account is that Maximian was the chief actor, petitioning Diocletian to resume his power. Lactantius’ account, by contrast, asserts that the elevation of Licinius was Galerius’ fait accompli, acceded to by Diocletian, and for which the presence of Maximian was quite incidental. Both accounts largely overlook the conscious role of Diocletian, yet the retired emperor was there to do far more than add lustre to Licinius’ appointment.

[…]

One cardinal principle of the Diocletian’s regime had been concordia, that is, the unity of the imperial college within the will of Diocletian.

Underpinning this concordia of the imperial college, and therefore fundamental to the unity of the family, was patronage. Each new emperor received the purple from the hands of his predecessor by adoption and nomination rather than force. It was precisely this principle which had been assailed by the ambitions of Constantine and Maxentius. To be sure, in the case of Constantine, Galerius had reaffirmed it by an adroit political manoeuvre to which Constantine had submitted in order to gain time to strengthen his position. Maxentius, however, had been offered nothing by Galerius save perhaps a fatal demotion, which he had wisely refused.

— Bill Leadbetter: "Galerius and the Will of Diocletian", Roman Imperial Biographies, Routledge: London, New York, 2009.

Since the Lactantius reference "mittit eum cum exercitu Maximiani ad expugnandi Maximiani filium" seems of special interest, it is in Lucius Caelius Firmianus Lactantius: De mortibus persecutorum (de mort pers, 26.8), on Wikisource rendered as:

Mittit eum cum exercitu Maximiani ad expugnandum Maxentium, et mittit Romam.

For the legalities that explicitly mention the idea of "his Caesar":

That was the beauty of the tetrarchic system: should any of the senior Emperors unexpectedly die, his caesar was prepared to take his place. It is true that in such case, as in the case of a sudden death of a caesar, there still had to be a discussion in the imperial college regarding the selection of a new caesar. But the death of an augustus automatically meant the promotion of his caesar to the rank of augustus. This was the essence of the Tetrarchy, this was how Diocletian wanted the system to work. Therefore, Flavius Valerius Severus was to become – and duly became – the new augustus in the West. (Fn_45)

Constantine was doubtless aware of the problem of legitimacy, as his feigned recusatio imperii indicates. It is also noteworthy that only Eusebius, Lactantius, Orosius and the two panegyrics claim that Constantine was made Emperor by the will of his father. Four other sources (Eutropius, Jerome, Philostorgius and Socrates Scholasticus) refrain from making such a statement, and the four remaining sources imply a decisive role of either courtiers (Aurelius Victor, Epitome) or the troops on the spot (Origo, Zosimus). Constantine, obviously, informed Galerius that it was the will of his father what made him accept the promotion. He may have lied, but it hardly mattered – such assertion was grave enough by itself, regardless of the truth. Here we should insert an interesting sidenote: what title was conferred by soldiers and courtiers upon Constantine on 25 July 306? Constantine would have acted very sensibly if he contented himself with the title caesar from the start. To preserve the Tetrarchy, this title had to be bestowed on someone anyway, since Severus now became the new Western augustus and thus a vacancy was created. Although it could be expected that Galerius would be offended when presented with this fait accompli, the lower title meant a better chance to be recognized. Indeed, some of our sources speak unambiguously about the rank of caesar: the panegyrics, the Origo and Zosimus. On the other hand, only Eusebius and Lactantius maintain that Constantine was made augustus, no less. The rest of our sources – Eutropius, Socrates Scholasticus, Aurelius Victor, Epitome, Philostorgius, Orosius and Jerome – indicate or imply the title augustus. If Constantine reached for the title augustus, he expressed both his lack of patience and his determination to unleash civil war, if necessary.

Fn_45: Barnes (2014: p. 68) rightly remarked that Severus „automatically advanced in rank from Caesar to Augustus when Constantius died“.

— Stanislav Doležal: "The Political and Military Aspects of Accession of Constantine the Great", Graeco-Latina Brunensia, Vol 24, No 2, 2019. doi

Posting here because comments are limited.

This is from my database of Roman Emperors, build for this timeline. I do not have the exact citation for this info, but bibliography for the whole database. Yet, I think this info might help you find your answer.