You don't need Bazzite to use the "steamdeck-like" interface. Any distro with steam will let you run Steam in "big picture mode" which will let you control steam with a controller.

That said, Bazzite will work fine, but you'll likely want to run it in desktop mode, rather than game mode. RPCS3 is just nicer to use this way, as it's not really meant to be navigated using a controller. Once you have your games set up, of course, you can play them with a controller.

As for running PS3 games, that should work fine. Your performance will likely vary from game to game, but a Ryzen 5 is "pretty good" for PS3 emulation.