Well, my NAS before was in the same style as yours and I moved it to that Linux Mini-PC (that by then had already replaced both TV boxes) because it has much better performance as a NAS (my router could only share using SMBv1 which has less than half the speed of SMBv2 and above, and there are even benefits for Kodi that is in that same machine to access the media directly via the filesystem rather than mounted shared, both because it's much faster doing full scans and because it will actually do proper incremental scans - i.e. only and quickly check files with creation dates newer than last scan data - when scanning my NAS for new media files.

As for shared MySQL synch, if I remember it correctly from when I read about it on the Kodi website, that's just having that MySQL set up as a standalone database server in a place accessible by all potential Kodi client instances and then configure your Kodi clients to use that standalone database instead of the internal database of each Kodi client.

This is just a traditional client-server structure were the "server" is the standalone MySQL database and the clients are the Kodi instances: pretty run of the mill way to have a server doing something for multiple client applications if they're all on the same network so lots of corporate software works like that.

The most obvious way of doing this is having that MySQL database on the Linux Mini-PC (even in professional settings, putting your database on a Linux machine is almost always the best choice) by installing it as a package (for example, with apt-get) and then you do have to initialize it and load it with data from an existing Kodi instance (again, if I remember it correctly, you export the data from the internal database of your Kodi instance and import it into that standalone database) and then point the Kodi instance (and any other present or future Kodi instances you want to use that shared watch history) to that standalone database. From looking at it (and given my experience with making server side software), I believe the instructions on the Kodi website for this are correct and complete even if they seem a little daunting at first.

Personally I didn't do it because I have no need for it and hence couldn't be arsed.