Even with Google's changes, F-Droid will continue to work with Android phones that do not use Google GMS.
If you care about your actually owning your device, install something else than stock OS. I would recommend GrapheneOS, since the security of some/most other alternatives is pretty bad.
As of now, Google isn't destroying non-Google android installs, so F-droid will still work there (correct me if wrong). So until Google takes android fully closed or succeeds in getting popular/necessary apps to blacklist non-Google-verified devices, F-droid still has a role
I hope so. The changes can mean two things: people can only use it easily in custom roms (I guess there is an overlap there) or they actually would play with Google: i guess technically they could as well register and sign the stuff with a Google key as the software is all FOSS and would allow defining another responsible developer (otherwise Google would have to through out all FOSS without CLA from their playstore). I guess quitting would be an option, but IMHO the outrage outside the bubble would probably be hardly noticable, so what would be the point?
If you care about your actually owning your device, install something else than stock OS. I would recommend GrapheneOS, since the security of some/most other alternatives is pretty bad.
Linus knew this day 1 and it bows to no one.
kernel is locked and most phones can't be rooted anymore