Psalm 121:3-4
אַל־יִתֵּ֣ן לַמֹּ֣וט רַגְלֶ֑ךָ אַל־יָ֝נ֗וּם שֹֽׁמְרֶֽךָ ׃[3]
הִנֵּ֣ה לֹֽא־יָ֭נוּם וְלֹ֣א יִישָׁ֑ן ומֵ֗ר יִשְׂרָאֵֽל ׃[4]
[3] μὴ δῷς εἰς σάλον τὸν πόδα σου, μηδὲ νυστάξει ὁ φυλάσσων σε.
[4] ἰδοὺ οὐ νυστάξει οὐδὲ ἐξυπνώσει ὁ φυλάσσων τὸν Ἰσραήλ.
[3] He will not let your foot be moved; he who keeps you will not
slumber.
[4] Behold, he who keeps Israel will neither slumber nor sleep.
יָ֭נוּם=yanum=νυστάξει=slumber
יִישָׁ֑ן=yishan=ἐξυπνώσει=sleep
The first one we have fewer surviving examples of. In Psalm 76:5, the same two words are used: נָמ֣וּ שְׁנָתָ֑ם, but with the 'sleep' in a nounal form as the object of the 'slumber'. So what we are probably looking at is a distinction English doesn't possess: between the process of falling to sleep, and the end result of sleep.
Slumber is an outright archaism. It's supposed to mean a light state of sleep, but people think it means a deep state of sleep.
https://books.google.com/ngrams/graph?content=slumber&year_start=1800&year_end=2022&corpus=en&smoothing=3
For example in this fascinating-looking YA comic book, "Slumber" is referring to a sufficiently deep sleep that you can set an entire Isekai story in it
https://www.google.co.uk/books/edition/Slumber_5/zPl6EAAAQBAJ?hl=en&gbpv=1&dq=%22slumber%22&printsec=frontcover.
Questions of the form "which translation expresses the original best" invite the answer "nope". That isn't something translations do.
The major translations on Biblehub (https://biblehub.com/psalms/121-4.htm) mostly stick to the ghastly archaism "slumber" but that's only because they don't know what else to do with it. The living language of English decided 200 years ago that it had one word too many for sleeping and it was going to dump the less common two-syllable one. Can't be carrying dead weight, right? Philological forces to contend with, what?
That leaves some dialects supplying dialect-idiom stopgaps. So we have "forty winks" and "getting some kip" and "catching some Zs" and "nodding off" and so on. Which the Imperial language immediately crushes into the lower mode of our speech.
A couple of the major bible translations have resisted: CEV has "doze" ISV has "take naps".
And the OP seems to be erring on the side of the Imperial master-language.
But English doesn't do these things in pursuit of refinement: it does them to keep its conquered language-families buying dictionaries and needing elocution lessons to gain employment.
CEV is designed for a lower reading-level, but to doze off is the gradual biological-physical process that יָ֭נוּם seems to refer to (going by the one useful example in Psalm 76). And it can be a noun: a doze.
And it's not really any less refined than any of the other barbarian grunty-noises we customarily utter up here in Ultima Thule.
The LXX's gloss νυστάξει is, nicely, that thing we do in the night (=νύξ). One isn't necessarily asleep yet (cf. Aristophanes Bird 639) or if they are it's a light sleep. So that supports all the above.
Aristophanes Birds, 639
Ἔποψ: καὶ μὴν μὰ τὸν Δί᾽ οὐχὶ νυστάζειν ἔτι ὥρα 'στὶν ἡμῖν οὐδὲ μελλονικιᾶν,
ἀλλ᾽ ὡς τάχιστα δεῖ τι δρᾶν
The Hoopoe-Bird: By Zeus! it's no longer the time to delay and loiter like Nicias;
let us act as promptly as possible....
