Did the Apostles “worship Jesus” in Luke 24:52?

Luke 24:52 NASB "And they, after worshipping Him, returned to Jerusalem with great joy"

Yes, the Greek word "προσκυνήσαντες" is talking about worship.

Here's the Greek word used: https://biblehub.com/greek/proskyne_santes_4352.htm

I am not an expert at all on hermeneutics but I hope this can help. The original word used is "proskyneō". The literal translation is "to kiss" or to lick as a dog does to his master. The same word is used frequently in the Gospel of Matthew. The Latin word used in the Vulgate is "adorantes", which also can mean "to worship" or "admire"

Matthew 28:9 And behold, Jesus met them and said, "Hail!" And they came up and took hold of his feet and worshiped (proskyneō) him. (RSV)

The word is also used as worship in the RSV translation of Luke

Luke 4:8 And Jesus answered him, "It is written, 'You shall worship the Lord your God, and Him only shall you serve.'"

Jesus says this to Satan when Satan is trying to tempt Jesus. He is referring to the 10 Commandments.

I believe that this is more of what the translator says it is rather than what the original text states. It is always good to look at multiple translations of verses you are unsure about. The original Greek is the best place because you can't straight up translate them. They have to make sense (which is why there is so many different translations of the Bible)

Translations for the word:
https://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=G4352&t=RSV

If you want a better answer, you should ask on the hermeneutics page https://hermeneutics.stackexchange.com/

The word used in the original Greek is pros-kyn-isan-tes ("[they] having fallen down and adored") and means to fall down in order to venerate someone (or a visible demonstration of veneration toward someone), and it is not necessarily (although many times) used in reference to worship of God. The English word "worship" comes from Old English weorþsċipe (woarth-ship), which means 'showing honor to someone by an outward action' (i.e. even kings, not necessarily God).

Hebrew also has a word for service or worship which can either be used of God or men (especially kings and such):

1 Chronicals 29:20 And David commanded all the assembly: Bless ye the Lord our God. And all the assembly blessed the Lord the God of their fathers: and they bowed themselves and worshipped [Heb. shtath-ḥa-hu/Gk. pros-kyn-isan-tes] God, and then the king.

So while not necessarily implying divine worship of God, it might in certain instances, with respect to Jesus the Son of God, indeed refer to divine worship. I think the lines are deliberately blurred by the Gospel writers in order to instil the idea that the Son of God, as such, is due the worship of God: inasmuch as in such instances as Christ is worshiped, oftentimes it is not always expected of mere Kings (e.g. Mt. 14:33).

There was some controversy over the phrase in the 80's because some minority of manuscripts appeared to omit the phrase which led to some Bible versions removing it or footnoting it. However, earlier manuscripts were found in the 50's that did have the phrase in it which make the later omissions likely scribal errors (mistakes). It has since been restored to the majority of the versions that had removed it because of this find. This is likely the reason why your version is missing it - if it's an older version.

Text Note: Luke 24:52

I will attempt to give you the reason the Greek (and now English versions) have the alternative that you stated.

In the best manuscripts the Greek states

24:52 καὶ αὐτοὶ προσκυνήσαντες αὐτὸν...

Literally this states, "And they worshiped him..."

προσκυνήσαντες is the aorist, active, participle which means it is a variant. The root would be προσκύνέω.

προσκύνέω has a range from "to do reverence or homage by kissing the hand" in the OT Septuagint but in the NT it means "to do reverence or homage by prostration (bowing or kneeling)"; to pay divine homage, worship, adore; "to bow oneself in adoration."

from The Analytical Lexicon to the Greek New Testament William D. Mounce

To your question about the Vulgate:

You translated this as "52 And they adoring went back into Jerusalem with great joy. 53 And they were always in the temple, praising and blessing God. Amen."

This is what the Vulgate states in Latin

24:52 et ipsi adorantes regressi sunt in Hierusalem cum gaudio magno

This translates to "And they worshiped him, and returned to Jerusalem with great joy."

It appears that whatever English translation you are using just did not translate the Latin word "adorantes" to worshiped but it still came close. If we go back to the Greek this is easier to see.

The operative clause is αὐτοὶ προσκυνήσαντες αὐτὸν.

1. In προσκυνήσαντες the ντ identifies it as a participle (participles are verbal adjectives as in they describe an action happening to someone or something)

2. The "σα" means that it is Aorist tense (a sort of past tense that means that it happened prior to now but doesn't specifiy time in itself)

3. The "ες" suffix means that it is identifying the adverb as describing the group (αὐτοὶ, "they").

4. We also know that a participle must modify something since if describes an action happening to someone or something and if there are only 2 nouns in the whole clause αὐτοὶ and αὐτὸν (αὐτὸν is singular and referring to a "him" and by context we know the him is Jesus) and the participle is plural and the only noun that is plural is αὐτοὶ (them) then the object of the participle (who it is being done to) must be the αὐτὸν (him).

In the translation you quoted above it doesn't make sense to say "And they adoring went back into Jerusalem with great joy." Here adoring is also a participle without an object. What were they adoring? If this were a verb, that is just an action the group was performing, then we would not expect this to be a participle and would have just been an plural, aorist, active, indicative (think time) form (as far as I know that form is never used anywhere in the NT).

There seems to be something missing as it is stated in your Vulgate version (not your documentation of it but an issue with the translation within it). Remember that the Vulgate was written by Jerome using the Greek so the priority should also go to the Greek text which clearly states that "they worshiped him..."

(All emphasis mine)