We identified a serious bug with F-Droid 1.16 through 1.16.2 when doing an Android version upgrade (e.g.: Android 12 to 13), causing F-Droid to end up in a broken state with no apps available and update checking not working.
We are preparing the release of F-Droid 1.16.3 which prevents this bug from happening. It will be out soon.
Please refrain from updating your Android version until you have updated to F-Droid 1.16.3.
More information and workarounds on https://forum.f-droid.org/t/important-f-droid-broken-after-android-version-upgrade/21902.