Do you know about Flatseal? It’s an application that lets you manage flatpak permissions. Until the portals system is fully working, weakening the sandboxing using Flatseal is what a lot of people do to make the apps work correctly.

Also, if you use KDE, the settings app has flatseal-like functionality built in.

Fedora has a pretty good amount of software in the repositories, so a lot of the time that’s enough. When it’s not, flatpak with flathub have most gui software covered, and outside of that, if we’re talking about terminal or command line stuff, most of those have their own custom way to install them, or they just have self contained binaries that you can put in ~/.local/bin/.

I haven’t run into many issues with flatpak like it sounds like you have, so that really covers a lot of it for me honestly.