It's a wrapper over Google Play not F-Droid. Much nicer interface, you can filter for things like ads/paid/GSF, you can bypass some regional blocks, you can login with Google accounts or use it anonymously etc.
I use Aurora droid. It is much better than just Fdroid. Search works well, updates are easy, and what is that? App pictures and icons actually load?? 😂 It generally is nicer to use than F-droid and you can add many different repositories to it including custom ones
BTW could anyone get it working on GrapheneOS? It crashes when I start typing a search request. (I've not tried the new version yet, but older versions installed from f-droid crashed.)
You might be blocking access to a specific Google Play Store domain or IP. I use Rethink firewall and experienced this when I was blocking a lot of Google's domains. I am using Lineage OS.