Try rebooting the Sonos app. If that doesn’t work, try rebooting your phone.

All Sonos does in their controller is send the request to Apple, and then display what Apple returns, so if there’s any interruption in that chain, you won’t see any results. It’s possible that Apple’s failing on sending back a result as well, although that’s relatively unlikely. 

I’ve rebooted the sonos system, router, phone with no fix. I have two apple accounts connected (which do not show), and several other services (which all show). 
 

Apple Music shows under services and I can play what I can access and play content successfully. Just no search results, apple doesn’t even show. 

Makes you wonder if there is an issue with Apple’s server not responding to the request from your Sonos controller. Have you checked with Apple?

No issues with Apple, just checked on another device and results appear. Deleted and reinstalled app on problem iOS device. Search results appear now. 

It really makes you wonder why the Sonos app doesn’t work better. 

The app doesn’t actually do the work, it’s the “app” running on your speakers, to the best of my knowledge. Which suggests that there could be some sort of wifi interference on your speaker, or perhaps a duplicate IP address which resolves, then unresolves, back and forth. 

But, if you’re in a situation in which it isn’t resolving / responding on one device, but it does work on the other, that certainly suggests something different, and then I’d submit a diagnostic from both controllers, and call Sonos and give them both diagnostic numbers, so that they could look at them and figure out why one is working, and one is not. The hard data in a diagnostic would be much better than any mental image we can build from your description. 

Had to delete, re-add, and re-Authorize Apple Music to all of my iOS devices with sonos. Some multiple times. What bollocks.