The music app is on macOS is insane half baked… it still chugs and has hiccups the longer it is left open during the day without restarting it.
Sometimes simple actions like add to a playlist doesn’t work.
Sometimes it’s possible to add a song twice and sometimes it does ask for the “song was already there, want to add it or skip adding this second instance” prompt.
The have concepts like “play next”, “play last”, “add to queue”… the last two are redundant but they appear in different instances.
Sometimes I’m listening to a song and just can’t restart it from the beginning with the “rewind” button (depends on the type of playback if it entered infinite mode or in station mode). I drag the time slider to the beginning.
The “next/history” songs panel just overlaps over the right side of the UI (if browsing album tiles, some of them will get half occluded)
Sometimes I can’t tap the the shuffle songs or the infinite songs buttons, can’t remember what happens exactly, but “they get gone”.
Annoying because on iOS it seems to work so much better and so much more pleasing to the eyes. Apple Music on macOS still feels and looks just like iTunes of the yesteryears.
I have some issues with the Music app.
1. Shuffle will bring up the same songs regularly. I have playlists of hundreds of songs and shuffling will do the same subset of them with a few less played ones here and there. This has been a longstanding issue going back to the 2000s though. Shuffle in iTunes/Apple Music has almost always been not random.
2. Searching for songs is generally poor. If I'm looking for a specific song, there are many times I cannot find it by searching. It exists in Apple Music, but I'll have to find it by going to an artist page or some other way. Searching is better on macOS than iOS, at least.
As for your raised issues -- I seen some but not all of them:
1. I don't have this happen. I have Apple Music up all the time (on my Mini it's been open for a week now and I can play and stop music without anything happening like you're describing on a base model M4 Mini)
2. I've seen that a few times over the years. It's not a new glitch.
3. I've not had this happen in at least 3 or 4 years, but it's also happened to me.
4. I don't use that feature much so cannot comment.
5. I've not had this problem. I can always go back to the beginning of the song that way.
6. That's an issue.
7. That's never happened in my usage.