To help clarify to GP (was going to help reply then saw yours) F-Droid is both the name of the core website hosting the APK repos and build infra, and the name of the Android client which can connect to any F-Droid compatible repo - there are a bunch of projects who host their APKs in their own F-Droid repo, all you have to do is go to their website and scan the QR code to add it or enter manually.

Signal could run their own F-Droid repo and people just add to their F-Droid client without using or touching the F-Droid website or build infrastructure at all, which would allow folks to do as lucgommans explains - one phone client connected to many repos, no manual downloading.

Example: https://www.bromite.org/fdroid