Hi @Gabriel,
I see things differently.
Bhava in dependent arising (and elsewhere) means a next life. It does not mean a sense of self. That is a modern interpretation but it doesn’t really fly if you look at the suttas as a whole. For example, the three types of bhava (kamabhava, rupabhava, arupabhava) clearly refer to the different realms.
See also AN3.76. Unfortunately Suttacentral now has Thanissaro’s translation, which I do not find very beautiful. I’ve written a bit about this before.
In a way upadana works exactly like the English: “take rebirth”, we say. Although in Pali you don’t “take bhava”, you do take up something (ie. “picking up”, “taking on”) because you crave that thing. That then leads to rebirth (bhava).
I think the prefix upa reflects direction. Ie. taking up. Then again, you can’t always give a prefix a meaning on its own. I think upadana and adana are effectively synonymous.
I’ve been fiddling around with “taking up” as translation and it doesn’t always produce nice sentences, but to me it’s more important to get the right meaning.
With kindness,
Sunyo