Generally speaking, the best way to access your media remotely would be to use a media server, like Plex, Emby, or Jellyfin. With Plex specifically, I know there are apps for macOS, Windows, iOS, and Android, but I don’t know about smart watches.
Does the smartwatch’s OS “app store” have a “File Explorer” (or something similar) available?
It might also be possible to just browse your server’s SMB shares with a simple file browser on the watch.
This is what I do with my Android and iOS devices to play music from my TrueNAS server. Such “file browser” apps usually have built-in music and video players. If it works for smartphones, I would assume such apps are available for smartwatches.
Again, bit outside of my tech knowledge here. I was halfway hoping to see if anyone on TrueNAS forums also has a garmin watch and managed to set this stuff up too.