The e-sim in a phone is a separate chip with proprietary firmware. The chances of a FOSS version of this HW are nearly nonexistent. It would require developing your own silicon and putting it into your own phones. Chances of FOSS FW for this proprietary HW are also very small, because it is difficult and there is not much reason to do so.
Currently, registering an e-sim requires a proprietary app (usually google). There is no FOSS alternative. Work on one is slow and there are some IP issues.
Using an e-sim does not require a proprietary app. So you can remove google services or remove their access to the e-sim HW once you have it registered. GrapheneOS uses this.
Well, this is a bit tricky to answer:
Huh, TIL, an esim is literally a sim soldered into the board.
Now I wonder, could something like the Pinephone FOSS modem firmware register a sim and resolve point 2?
I am not an expert but I don’t think a modem has anything to do with registering the e-sim.
Even if it did, the hard part is probably getting the e-sim data/keys to be registered, not the uploading it to the e-sim chip itself.