Hey The_Panda_Man_!
It appears you have some access issues in the Music app when you search Apple Music. We also noticed that you are missing the 'For You' and 'Library' tabs at the bottom of the Music app. We'll do our best to help you out.
- Check that you're signed in to the same Apple ID used for Apple Music on each device.
- We'd make sure to check that cellular is active for the Music app in Settings > Music and that Cellular Data is on. Same in Settings > Cellular > Music, make sure it's on.
- Go to Settings > Music > "Show Apple Music" and "Sync Library" should both be enabled.
If you continue to have these issue, check on that subscription to ensure Apple Music is active in Settings > [Your Name] > Subscriptions.
Resource to check next: Join Apple Music on your iPhone, iPad, iPod touch, Mac, or PC
We hope this resolves your issues. In case it doesn't, tell us if you continue to have this same issue after connecting to a known good Wi-Fi network.
Take care!