I haven't used OneDrive specifically, but I have gone through the process of trying to use the same music library on two computers via an external hard drive. Additionally, I sync my playlists to an Android. I've gotten all of it to work, but there were some quirks I'll share (some of which you've run into already):
1. You can change the paths in each instance of MusicBee for different drive letters, but as you stated there are no options to make the built-in playlists relative path. Being an external drive, I just remapped the letter on the second machine.
- I'm not certain if this would work, but could MB load exported M3Us as built-in ones? I see you can change the built-in playlist type to M3U, so maybe you could export on the first instance to a folder, then point the second instance to that folder for its built-in playlists? It would still require manual exports every time you change something, but without relative paths in built-in playlists or changing drive letters I'm not sure there's a fully-automated solution for the playlists specifically.
2. Both instances should automatically respond to changes in a song's meta tags, but when adding/deleting a song you'll need to rescan in the other instance. You can setup automatic scans on whatever folders you like and dictate whether new files go into the inbox or the library.
- You can do this in Edit->Preferences->Library if you haven't already, but note that while you can monitor multiple folders all of them are added to a single location (ie, library or inbox). So what I would do is designate one instance as the "add new music" instance and set that one up to continuously monitor a folder and add to inbox (for entirely new music). Then on the second machine, set up the continuous monitoring to add directly to the Library (the assumption being that any new music will be added on the first instance). If you add or delete anything on the second instance, you would have to manually rescan on the first instance since it is looking at the inbox folder normally.
3. File naming can also cause some hiccups if the two instances aren't configured the same. If you decide to apply a naming scheme to the files or auto-organize them a certain way, make sure you're duplicating those settings on the second machine so they aren't constantly moving and hiding files from each other and creating dead links.
In my particular case, I was using a different PC for several months, then returned to the original, rather than using both simultaneously. But if you set up one computer as the designated computer to add/delete songs and edit playlists on, it wouldn't be too difficult to have any number of others auto-scan for changes and update.
Hope some of that helps.