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.

Bazzite only really does gaming mode on AMD GPUs (RX4xx+). As a general rule of thumb AMD cards are usually better supported under Linux. Bazzite's desktop mode should work fine on a 1660 though.

You don't necessarily need Big Picture mode like on the Steam Deck, in fact i think your current Nvidia card might have issues with it https://docs.bazzite.gg/Handheld_and_HTPC_edition/Steam_Gaming_Mode/ You could use another distro like Fedora, install Steam and just set it to launch in Big Picture mode

Have a look here:

https://rpcs3.net/quickstart#supported_devices_pcs

AMD GPUs have better all-around compatibility on Linux, but if you're mainly gaming, Nvidia GPUs can be made to deliver good performance as well.

Specifically for ps3 emulation you would benefit from having as good a cpu as possible.

An R5 2600 is listed as D tier on the rpcs3 CPU tier list.

Anecdotally thats the same cpu I use in my windows media computer in my living room. I've tried to do ps3 emulation on it quite a bit. It's a little hit and miss but mostly miss. I can somewhat get away with playing easy to run games but anything even remotely difficult to run is unplayably slow. And I've got an RTX 3060 ti in that. That GTX 1660 is not going to help things.

Gamescope (what steamos/bazzite ect use for their big picture mode) and Nvidia proprietary/open drivers is a bad combination, while nouveau has shit performance at the moment. Stop asking and start testing.

I would trade that GeForce GTX 1660 for a Radeon RX 6600 (these are cheap too) because NVidia doesn't work well with gamescope (SteamOS/Bazzite big picture console mode).