Tekken 7 is on Steam and rated gold on ProtonDB. However the minimum system requirements look to be pushing your system so I don't think you should bother with it. Definitely don't try emulating it as that's even more difficult.
Tekken 3 you can indeed emulate on the PSX. Download Duckstation from Flathub and learn to set it up. An alternative to Duckstation that can play more systems is RetroArch.
Find the game from the ROMs Megathread or Vimms Lair.
Good controllers that work on Linux can be found from Gulikit, 8bitdo, Retro Fighters.