Why is Apple Music using up half a gig when I have no songs, and have deleted the app?

Thank you for the image.

You could reinstall Music and see what's there. Maybe some podcasts or music that's been placed there by other apps. And then delete it. Maybe that will clean out the data.

For example, I restored my current phone with Migration Assistant (?) from a previous phone. However, there is an app that I did not bother to download to the new phone even though it was on the old phone. That app shows it has 2.8MB of data even though it has never been installed on this phone.

If you have a Mac then you could connect the phone to the Mac and look at its contents with the Finder (assuming a newish Mac OS).

Or you could use iTunes on an older Mac.

Or you could use Mac or PC software that allows viewing the contents of the iPhone eg PhoneView, iMazing etc.

Thank you for the image.

If the app has been off-loaded then its data will still be on the device. You could download the Music app and check for music.

Please post an image of the top third of the screen at Settings > General > iPhone Storage

Tap on the 414.9MB and what does it show? Please post an image.

Have you been the only owner of this phone? Did you restore it from a backup of a previous phone?