Hello and welcome to Apple Support Communities Rommerei,
I see that you're getting a message that your songs are not available in your country/region. I listen to music on my devices all the time, so I certainly can understand wanting to get this resolved, and I'd be happy to help.
First, when you switched to the new iPhone, did you change your country/region settings for your Apple ID account? The article below can guide you on how to check on these settings, if needed. Just changing devices should not affect the country/region listed for your Apple ID account.
Change your Apple ID country or region
If everything is set correctly and has not been changed, go to Settings > iTunes & App Store, tap on your Apple ID and sign out. Once you're signed out, restart your device and go back to Settings > iTunes & App Store and sign in.
This step will temporarily remove any music you’ve saved for offline listening, you will have to redownload all the music saved for offline manually again. Once thats complete, check to see if you play the songs without getting the message again.
Let me know how this goes.
Have a great day!