This is a great question. I guess a good starting point is to uninstall the software and see what files remain behind.
As you noted, Database is the big one. Fortunately that folder does get left behind so if you ever have to re-install the software in a pinch it’s very useful. In my experience I would also include User Management and if you’re using Driver Framework you’re going to want to backup the drivers as well. The latter is in C:\Program Files (x86)\Tecan\FluentControl\LegacyDrivers. However those two may not be so Git friendly.
Historically the Fluent Control has had a tendency to crash during development so I’ve always been mindful of VisionX and SVNRoot. I’ve brought back more than a few computers from the grave with just those two folders.