The Greek letter is usually spelt bêta. But the use of the word as in version beta is indifferently spelt with or without the circumflex.

• Android 12 : comment installer la version bêta du nouvel OS

• Logiciel en version beta

Anyway whether bêta ot beta it is still pronounced [bɛta].

If you look at the wiktionary it says:

beta
(Non standard) Variante de bêta.
Les cellules beta.

The ê letter has been chosen to represent the ancient Greek ῆ (êta) of βῆτα (modern Greek ή). It corresponds to an open long vowel [ɛː] while AmE uses [eɪ] and BrE uses [i] instead ¹.

The French circumflex mark here the length of the vowel and not a letter that would have disappeared.

Êta is also present in these other letters from the Greek alphabet:

zêta: ζῆτα:

êta: ἦτα

thêta: θῆτα

No accent is needed with delta because of the following l. The Greek vowel is different too (epsilon representing the short closed vowel [e]): δέλτα

An acute accent is required in the last Greek letter to represent this same [e] in French:

oméga: ὦ μέγα

¹ _{For english usage, see Why are Greek letters pronounced incorrectly in scientific English}