I've been using arch for a while now and I always used Flatpaks for proprietary software that might do some creepy shit because Flatpaks are supposed to be sandboxed (e.g. Steam). And Flatpaks always worked flawlessly OOTB for me. AUR for things I trust. I've read on the internet how people prefer AUR over Flatpaks. Why? And how do y'all cope with waiting for all the AUR installed packages to rebuild after every update? Alacritty takes ages to build for me. Which is why I only update the AUR installed and built applications every 2 weeks.
I use Silverblue and in general I like their philosophy. For other distros, it can be summed up as:
Flatpaks for GUI applications
Your choice of package manager for everything else
On Silverblue anything non-Flatpak is best installed inside a container. On a non-atomic distro I'd just install using the system's default package manager.