This app was mentioned in 2 comments, with an average of 8.50 upvotes
I really didn't want to scroll through my long list of old apps because I thought I wouldn't recognize the app. But it's literally called Random Music Alarm. So thanks for your comment! I needed a little push.
there's a fairly unknown korean alarm clock that plays random music and has gradual volume increase. I used it long long ago and didn't have the rest of your requests, but maybe it does now