A few months ago, Proton’s CEO Andy Yen was interviewed on The Linux Experiment and reiterated in the segment starting at 49:27 that he does want to have an F-Droid version, but because Proton encrypts notifications sent through Play Services such that Google can’t get at the metadata, and because third-party notification frameworks are typically much worse for battery life than Play Services, they consider F-Droid a lower priority than some of the other things they’re trying to get done, such as feature parity between their mobile and desktop apps. It’ll come eventually, especially as Yen himself seems to want it, but since they’re completely private and have no investors, they don’t have infinite money for developers, so they have to prioritize sustainable growth.
Highly recommend watching the full interview, Yen seems to have a good mindset about the whole thing, doing what he feels is best for privacy and ownership of identity in the long run, even if he has to temporarily compromise in some places in order to get there.