You can run Jellyfin on the Ryzen 3600 machine and point it to the NAS movie directory. At least to try it out (Alternatively, throw some movie files on the machine locally as a test). Then just use the Jellyfin frontend (http://localhost:8096/) on the same machine as the media player. Then also try if you like using it via Jellyfin app on the phone

Only on Linux, because the HDMI forum didn’t allow AMD to write an open source driver with HDMI 2.1 features

Depends a lot on the game, Ridge Racer 7 is easy to run for example. Playing it on 5600X + RX 6800 at 4x scaling with rock solid 60 FPS. I’m sure some powerful phones could run games at native res and 30 FPS