I would recommend Obtainium more than F-droid: https://github.com/ImranR98/Obtainium
F-droid is just as centralized as the PlayStore. They just have different rules (open source only) but can easily take down an app just because they want it down.
With things like Obtainium, you download the APK straight from the Amethyst repo. There is no list.
F-droid is useful if you want curated ooen aource software that has at least met some minimum aet of privacy requirements. Its good for people starting out, not knowing how to identify credible ooen source apps.
I'm curious why nobody mentions that you can install your own app repository and pubkey in f-droid? nostr:npub1lxktpvp5cnq3wl5ctu2x88e30mc0ahh8v47qvzc5dmneqqjrzlkqpm5xlc
I don't think they care about privacy. F-droid is about open-source. While I am sure they also like privacy, it has not an issue to accept non-private apps in their catalog. The proof is that Nostr is not a privacy-first protocol but it is there.
