The server certainly should have picked up the change in metadata but I can’t help you with why it didn’t.
I can suggest that you edit the metadata in Jellyfin rather than using external tools and moving items in and out of the library. Just click the three-dot menu for a track or album and choose “Edit metadata”. If it doesn’t pick up changes made from Jellyfin then something is very wrong.

If you can avoid having you server and the media library on separate systems you should. That means buying (or I suppose building, but I wouldn’t recommend it) a NAS with sufficient processing ability to stream / transcode as much as you need, or stuffing a lot of storage into your mini PC.
One of the problems you’ll run into if you use separate systems is that it’s non-trivial to get the server to automatically notice new items in the media library and update to include them. I’m sure there are others.

So this WON’T break the “Jellyfin” Kodi plugin? Just making sure it’s not the same thing as “Jellyfin4Kodi”.