"Play Next" in Music App Not Working

Since the 16.4 update, certain elements of the Music app have been either not working well or not working at all on my devices. When I try to start playing one of my playlists, there is about a 20-second delay before the first song begins playing (this was instantaneous before 16.4). If I try to play just a single song, there is no delay. Also, if I try to use the "Play Next" feature from within the playlist, it freezes for a bit and then continues but does not play the next song that I asked for. I am seeing this behavior on my iPhone 13 Pro that is now on 16.4.1. The MacOS Music app is not showing any of these problems. I've seen many others reporting problems with the Music app since the 16.4 update, but not exactly what I've been experiencing, but I figure they are probably related.

[Edited by Moderator]