No, there is confusion, this is a pretty long thread and a lot of posts, so I'll do my best to make this as coherent as possible.
Part 1:
I have two MacBooks (MacBook Pro 2015, and MacBook Pro M3). My MacBook Pro 2015 only runs up to Monterey. I noticed the sync issue then when I tried to sync with my MacBook. I thought it could have been a Monterey issue.
When I got my MacBook Pro M3, I saw that the sync issue persisted (Sonoma). So I knew that this wasn't likely to be a macOS issue, but rather an iPhone related issue.
I only sync my iPhone 15 with my new Mac, as syncing with two Macs would just cause all sorts of headaches and it wasn't intended to be done.
Part 2:
As for manually copying music. It doesn't allow me to manually copy music (by selecting 'copy to device') if music management is turned on in Finder. Once it is turned off in Finder, it works perfectly (I tried it on my iPad, since I don't want to risk messing up my iPhone music library before there is a fix for it). It not syncing by selecting 'copy to device' makes sense if the music management is being managed in the Finder, so it wouldn't allow music to be added outside of the Finder.
Part 3:
As for the iPhone Sync, there are two options in the Finder. (Backup now, and Synchronize). Hitting either one initiates the 5 steps. The only difference (if I remember correctly) is that hitting 'synchronize' allows the option to skip the backup. So either way, it has to go through the sync process, where it gets stuck as mentioned in this thread.
To be fair, I don't really remember what the difference between 'backup now' and 'synchronize' is because I haven't done a manual backup in a while (my devices have hundreds of gb worth of data). I think I will try the two options with my old iPhone 12 on my old MacBook 2015. (Since the iPhone 12 has about 15gb of data and I can confirm it syncs correctly, given that my AppleWatch isn't paired).
This issue just became a rollercoaster of confusion. Hopefully, the above cleared it up. Regardless, the issue is still what the thread is about. Considering this thread is nearly up to 19k views, I have hope that this issue will be fixed soon.