Games from Steam will work with just about any controller, non-steam games can usually be made to work by launching them from within Steam, so add the games to Steam when installing through Heroic or Lutris eg.
One possible issue is that mixing rpm & flatpak runtimes can cause issue’s with Steam Input, atleast it did for me on Fedora 38 where Heroic installed as a flatpak couldn’t interact with Steam Input where Steam was installed from rpm.
Maybe, but consider this, you can dress up for colder weather, the same can not be said for hot weather, there’s only so much you can leave off (legally)