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There is meager information on both the background of the Šu-tu and the background of the Hyksos, so any attempt at connecting the two would probably be highly speculative.
With that said, it's possible that the maps are (loosely?) based on Manetho as quoted by Josephus:
"...This whole nation was styled Hycsos, that is, Shepherd Kings: for the first syllable Hyc, according to the sacred dialect, denotes a King: as is sos a shepherd: but this according to the ordinary dialect: and of these is compounded Hycsos: but some say that these people were Arabians." (Against Apion I, 14)
According to this, the Hyksos were "Arabians". It should be noted that the terms "Arabian" and "Arabs" at the time of Josephus was used loosely. Josephus also referred to Kharetat (Aretas), king of the Nabateans, as an "Arab" (Antiquities of the Jews XIII, 13:3), and the same goes for Ovdat (Obedas) (ibid. 5).
On the wideness of their territory, it has been suggested in the past that this was more or less the size of their empire, post takeover of Lower Egypt:
"In older scholarship a vast empire of the Hyksos was imagined, since finds with the names of rulers, especially Apophis and Chayran, were known from such far-flung areas as Knossos, Boghazkoi, and Baghdad. Later this distribution was explained as exported art or as war booty. In reality it seems the Hyksos rulers used a special gift culture to retain loyalty through a sort of indoctrination of the elite. This practice is attested by the bronze dagger of Nakhman, the writing palette of Atja (Morenz 1996: 167–70), and various perfume containers. These gifts sometimes bore highly poetic glorifications of the king." (A Companion to Ancient Egypt, p. 105)
Your maps stop short of the edge of Babylon, though.
On a possible connection with the Šu-tu, Lloyd Graham in his essay "Which Seth? Untangling some close h*m*nyms from ancient Egypt and the Near East" suggested etymological connections between "Šu-tu" and the main deity the Hyksos worshipped in Avaris (their capital in Egypt), Set or Seth, the god of foreigners (which is what the Hyksos were in Egypt). However, I don't think there's evidence beyond possible etymology to connect the two. The Bible itself names a great many distinct ethnic groups that all lived at one time or another in the supposed homeland of the Hyksos or in its vicinity.
Side-note: I wonder if the second Megiddo is a misinterpretation of Joshua 12:7 which says: "And the following are the kings whom Joshua and the Israelites defeated on the other side of the Jordan seawards" and then lists the king of Megiddo in verse 21, with seawards maybe being understood as a reference to the Dead Sea?