Some thoughts about birth and existence, looking at the definition in SN 12.2:
“And what, bhikkhus, is birth? The birth of the various beings into the various orders of beings, their being born, descent into the womb, production, the manifestation of the aggregates, the obtaining of the sense bases. This is called birth.
“And what, bhikkhus, is existence? There are these three kinds of existence: sense-sphere existence, form-sphere existence, formless-sphere existence. This is called existence.
In English, we use birth metaphorically, we can say things like “she was born into a position of power”, “he was of noble birth”.
It could be that birth is used much more literal in Pali, like in the definition above, it involves a womb, production, getting aggregates and sense bases.
But clearly, there are ways to exist that don’t involve a womb, like the antarabhava, or the heaven realms where you spontaneously appear instead of getting there via a womb.
Another things is that according to the second noble truth (SN 56.11), you can crave for bhava - if you don’t believe in rebirth, you still very much crave to maintain your personal existence, materialists have bhavatanha too.
So it makes sense to me to translate bhava as existence.
Also, in dependent origination (SN12.1), bhava is the condition for jati. No existence, no going into wombs.
But you can have bhava without jati (in the short term, e.g. antarabhava), while any kind of jati implies bhava.
There’s also the fact that stream-winners declare the end of “the animal womb” (AN 5.179), while the arahant declares the end of bhava.
To sum it up, maybe in Pali a rebirth into a jhana realm would be bhava but not jati, but in English ‘birth’ is already broad enough to cover all cases.