Real Bible Translation

And the Cowering One became to die and to be carried off by himself below the Angels into the Fold/Gulf of Father of Multitude ("Abraham"), and the Rich One also died and was buried.⁶²

Julia Smith Literal 1876 Translation:
And it was, the beggar died, and was carried by messengers into Abraham's bosom: and the rich one died also, and was buried;

LITV Translation:
And it happened, the poor one died and was carried away by the angels into the bosom of Abraham. And the rich one also died and was buried.

ESV Translation:
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Footnotes

The phrase Ἐγένετο ἀποθανεῖν καὶ ἀπενεχθῆναι αὐτόν (Luke 16:22) may be analyzed in two ways. Grammatically, it consists of the aorist middle indicative ἐγένετο ("it/he came to be") governing two aorist infinitives, ἀποθανεῖν ("to die") and ἀπενεχθῆναι ("to be carried away"), with αὐτόν ("him") as the accusative subject of both infinitives. It has been interpreted as idiom, or what is called, a periphrastic infinitive construction with γίγνομαι + infinitive(s). It is unusual, but was considered to be meant for the narration of events in a formal, almost liturgical style, i.e. "And it came to pass...." Such a phrase would not be used in normal dialogue—periphrasis refers to the use of more words to express a concept that could be conveyed more simply with a single word. But was that the point? In the very same verse, the simple word is used of the rich man, "and he also died."

A strictly formal rendering would be: "It came to be to die and to be carried off by him."

Carried Up or Carried Off?

ἀπενεχθῆναι αὐτὸν does not mean "carried by him." It means "to be carried away by him" or "to be carried off", with the emphasis on the subject being the one who is carried away. The word αὐτὸν seems to be skipped over/deleted by other translations.

The verb ἀποφέρω (and its derived forms) generally means "to carry away," "to bring back," or "to take away." While its basic meaning is neutral, it carries numerous negative connotations depending on the context. In some uses, it describes the act of carrying off spoils or losses (e.g., ἀπένεικαν τεύχεα –

"They carried off the armor," Odyssey 16.360),

or the dissipation of something, as in ἀπενεχθέντες ἐς Λιβύην –

"Having been carried off to Libya," Thucydides 7.50).

These suggest negative outcomes, such as loss or theft. Additionally, the verb is used metaphorically to indicate paying back or returning something, often in contexts of debt or punishment as in ἀπήνεγκε παρανόμων –

"He handed in an accusation," Demosthenes),

which can carry the weight of unpleasant repayment. Lastly, it can describe the returning of individuals, such as a sick person being carried home, again often implying a tragic or unwelcome return (e.g., ἀπηνέχθη εἰς . . ἔτι ζῶν – "He was carried back while still alive").

(See Logeion ἀποφέρω)

Thus, ἀποφέρω is simply not the right word to express "carried by angels" in a positive sense. Instead, ἀναφέρω or ἐπαναφέρω would be more appropriate, as both verbs have meanings related to raising up, lifting, or carrying in a more neutral or positive sense, and can be used in contexts involving divine or heavenly beings.

ἀναφέρω (to carry up, to bring to) can convey the idea of being lifted or raised up, which aligns more closely with the notion of being carried by (good) angels.
ἐπαναφέρω (to carry back or to restore) is also a possible alternative in certain contexts, though ἀναφέρω would be a better fit for something like "carried by angels".

For example, if you want to say "carried by angels," a better translation would be ἀναφέρεται ὑπὸ τῶν ἀγγέλων or ἀναφέρεται ὑπὸ τῶν ἀγγέλων depending on the tense and nuance.