Well, I solved it. Apple is responsible because it still, inexplicably, has no exclusive mode on MacOS. Just iOS. I use a little app called LosslessSwitcher to make up for this oversight.
So, to see if another music service would be involved, I got a 30 day trial of ABigJungle Unlimited (AMU). AMU still sucks, except it does have exclusive mode and Apple Music does not. This lack of exclusive mode on AM was a clue on the cause of it launching on its own!
Anyhow, when a SONG on AMU changes (at end or, me skipping), Apple Music launched!
Remember, this was happening before I installed AMU but this suggested a clue.
Just to check, I quit LosslessSwitcher I use to automatically change bit rate in AM and, the launching stopped! So LosslessSwitcher is the culprit!
Now, if only Apple made MacOS like iOS has been in this respect, we can get on with our lives…