I have also had very similar (I hold back from saying the same exact) problem. I also assumed that the library on my iMac would rule the cloud. Not so. I would repeated make changes — playlist contents, playlist folder organization, and so one, meaning to update the 'master' copy on iCloud. No way, no chance. Just like you reported, Choosing the File-> Library-> Update Cloud Library menu item, made things runs backward. Instead of updating iCloud, this option runs in reverse and updates the local library to 'match' what is in iCloud. Like you, discovered that when I created a playlist on an iPhone, *then* it *did* appear in iCloud. it was like, the iPhone rules and the MacOS Music program takes its orders from …. Where? This is a major fail point in my estimation because, there are lot of things you simply cannot do on the phone. Playlist folders are great, but you can't create them on iPhone *or* put playlists into [move] playlist folders on the phone. Maybe there is some [non obvious, at least to me way to do this? Creating smart playlists and managing folders is completely beyond the realm of the iOS Music app. Taking this as a given (that is, it’s right until some helpful person proves it otherwise), then why oh why Apple, would you make it the menu function File-> Library-> Update Cloud Library not actually work. If it *does* do it is supposed to, then it is grossly mislabeled.
So I following some vague hints with some skepticism that this is what should work, I disabled the sync to iCloud option on iMac, logged out of iCloud, [ a much bigger deal, imo, pretty much disabling my iMac] logged all devices out of iCloud — a major pain — btw, rebooted the iMac, and turned off my iPhone and iPad — just to be sure — they were rendered clueless. Then, restarted the iMac, only, logged back into iCloud, started the Music app [all other devices were off at this point] then toggled the Music “sync to iCloud option”. Then I could make changes and the update to iCloud option worked briefly. I say briefly because after restarting the iPhone and iPad, iMac Music app was no longer the ‘master’ of the iCloud Music library.
TL;DR Music app on MacOS cannot update iCloud Music library if any iOS devices are logged into the same Apple ID/iCloud/Music account/library. In that case, MacOS Music app option to update the iCloud library, does not work. This situation is effective with Monterey 12.1 and I wish it were not so. Please help me by pointing out a less drastic ‘workaround’ then the one I discovered. I would appreciate that so much. I am working on a project and for the time being, my work around is to ditch us of the cloud library all together. That work around is way too drastic and time consuming for more frequent use
