Generally it's simpler if you have your NAS separate from your application server. Synology runs NAS really well, but a separate application server for docker/etc is a lot easier to use and easier to upgrade than running on Synology. Your application server can even have a GPU for media transcoding or AI processing. Trying to do everything on one box makes things more complicated and fragile.
I would recommend something like Debian or NixOS for the application server, and you should be able to manage it over SSH. You can then mount your NAS as an NFS share, and then run all your applications in Docker or NixOS, using the NAS to store all your state.