Yes, I learned earlier today that you apparently need to be running iOS 13.2 (released just last week) to get this to work under the Home app. I was using iOS 13.1 on my iPad and there you can enable an automation to play music on the HomePod at a specific time but it requires that you confirm the automation every time before it will run (at a particular time). So, not useful to create a wakeup music alarm.
Unfortunately, although iOS 13.2 allows you to create an automation using the Home app (in addition to the previous support for automations under the Shortcuts app) it requires that the music source be from an Apple Music subscription and you can't enable this feature using your own music even if that music was purchased directly from the iTune Store.
So, the only way to create a wakeup music alarm is that you pay Apple a monthly subscription fee. And note, none of this is required when I set alarms on my Google mini. You just need to say something like, "Hey Google, set an alarm to play some music at 7:30AM." And I make no payments to Google to do that.
I don't know about Apple's Music service. I tried the free trial last year and I found it to be worse than the service that I get for free from Pandora. It's not the size of the music library that is the problem, it was the fact that Pandora did an immensely better job at selecting music that actually matched my preferences.
Apple Music would mix in totally inappropriate tracks during playback of something like classic rock, it was almost like they were trying to "push" certain music genre like rap or hip hop because those were the "hot" tracks of today. Believe me, Apple, rap is NOT classic rock. In fact, I think they even did that same substitution when I asked for country music.
I don't know, maybe Apple has improved their algorithm in the last year or two. I think they are offering a new (second) free trial so maybe I'll give that a try.