Adding a library to Remote app on iOS 16

This problem was solved by deleting and reinstalling the Remote app on the affected iPhone. Once done, I could see the iPhone in Music's list and manually pair it to the Mac using the code generated.

My library's running in Monterey, which may or may not be significant. As I've had no connection problems with a couple of devices running older version of iOS, iOS16 is likely to be the culprit though. FWIW, I do wonder if Apple remains committed to Remote. It hasn't changed much in the six or so years I've been using it and it now frequently conflicts with the Music (or iTunes) app running on the same network. My gut feeling is that Apple will soon be deprecating it (iOS17 perhaps?) in favour of the Music app which will do the same job and maybe, through some new Apple (of course) hardware that includes a DAC, allow us to stream from a shared networked library in true HiFi over Airplay rather than AAC which is the current streaming codec. Not that there's anything intrinsically wrong with Apple AAC!

Yes I understand. Remote makes that much easier!