The are stack itself is so low power that you absolutely can run it on a NAS like synology for example… I mean you can run a Plex server on a NAS and it actually works so…
In my case I have it seperated. I have a NAS that does absolutely nothing else besides being a NAS. I then have my mediaserver for the are stack and jellyfin.
So that could be your Pi, and the you get an old used Synology for example.