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.
Would love to ditch google and use grapheneOS, however have so many banking and (stupid) outlook for work.
This piddly open source effort pales in comparison to what we should really be doing:
Horizontally splitting Google into multiple companies.
Not division via department splits, but equal partitioning across the company into multiple horizontal businesses that compete on the same offerings.
The EU and next DOJ/FTC need to force this.
GrapheneOS works only with Pixel devices, which doesn't make it much useful for the vast majority of Android users.