Could be any number of those things you mentioned! One tip that helped a few people is to reset the phone network settings, but just bear in mind if you do this it will change your phone name back to default (Go to General/About to change it back) and remove all of your saved wifi passwords. Also checking what streaming rate you have configured in the Apple Music settings to check the cellular connection can handle it; maybe dropping down from lossless if that’s currently selected on cellular.
For me that didn’t work, and I continue to have skipped songs, times when it just refuses to play, and this is on CarPlay and Apple Watch, even in areas with strong cellular reception. I also get an error message when trying to play some curated stations as well, so I think Apple Music is quite buggy, as I only started having these issues on ios16. I’m using Spotify for the moment, until it’s hopefully sorted out, as I can’t handle messing around with my music when out on a run or whilst driving.