For devices such as iPhone, iPad, Mac, no the Music is not one of the supported apps for Handoff.
- Apps that work with Handoff include Calendar, Clock, Contacts, FaceTime, Freeform, Keynote, Mail, Maps, News, Notes, Numbers, Pages, Reminders, Safari, Stocks, and many third-party apps.
Use Handoff to continue tasks on your other Apple devices - Apple Support
Since your tagline shows HomePod, that does allow to do some other things:
- Transfer music playing on iPhone to HomePod by tapping it to the top of the HomePod.
- Transfer music playing on your HomePod to the iPhone by placing it near the top of the HomePod and accepting the transfer prompt.
You can send Feedback to Apple here:
Feedback - Apple Music - Apple