Thanks for sending the screenshots and for sharing the additional information, Olaf.
As you’ve said, the cloud status for the tracks you shared does say "Purchased, and the files are listed as a “Purchased AAC audio file”. Since the tracks work as expected on your Mac (e.g., without DRM-protection), and this information was taken from the track info on your Mac, then we can assume somehow in the process of the files being transferred to your iPad, it may be that Apple’s iCloud Music Library listed these tracks as DRM-protected when they shouldn’t be.
For this reason, the next step to troubleshoot this would be to try syncing the music from your Mac to your iPad using a cabled connection to do so. This should hopefully allow the iPad to see the tracks as Purchased, as they currently are seen on your Mac.
For more information about how mix-ups like these can happen when using Apple Music (streaming service) and the iCloud Music Library, here are some outside resources that also offer additional troubleshooting steps which you may find helpful:
Apple Music problems? Here’s the fix!
Seeing “Apple Music” instead of “Matched” on your iTunes tracks? Here’s the fix!
How to check your iCloud song status
Please let me know if these troubleshooting steps solve the issue for you!