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?

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.

what do you even mean?! start what at the kernel?

kernel is locked and most phones can't be rooted anymore