My setup is that I have my Kodi DB on my NAS in a MySQL DB with multiple Kodi devices sharing the DB.
It’s not apparent to me how to have Sonarr update the MySQL DB directly (without Kodi running). It looks like the Kodi Connector is designed to talk to Kodi (which would update the DB). However my devices power down when not in use so I can’t be sure a Kodi instance would be running. Can the Kodi Connector talk to the MySQL DB directly?
I don’t know what your NAS is capable of, but you could consider running Kodi headless on it. Presumably your NAS is always on so you can have sonarr talk to that instance to perform updates.