

Keep the synology as a high-uptime nas.
Im not sure which Linux district is best for gaming and running docker with an nvidia card. I just run NixOS for everthing, but that requires a lot of coding.
You should be able to keep running Linux mint on there. You can install steam and Delfin for jellyfin on there, both are available as flatpaks. You can connect the nas using NFS to /mnt in the machine using the fstab. For running the jellyfin server, I would install it using docker compose and put all the files for jellyfin in the NAS.
If you dont want to game, you could Sell the GTX 1080 and buy an Intel a310 for €100 (faster for transcoding and better Linux support).
Yeah, that’s fair. Nvidia gpus don’t support linux well but it’ll work well either way.