Music app stops playing on M1 Mac

Macbook Air (M1) with Big Sur 11.3 (20E232) and Music 1.1.4.110

I created a new Music Library when I got the new computer by adding files that were already in Apple lossless format (files I'd previously converted from CDs). If I play them through the computer's speakers, it works just fine.

If I try to play them via any Airplay device (e.g., to a fully up-to-date Homepod, or to an old Airport Express), Music stops playing after after a few songs. If I double-click on the track, it starts playing again.

In contrast, if I play music from my iPhone to the same Homepod or Airport Express, it works just fine. The files on the phone were synced from the files on the Mac.

I've deleted all music preferences; rebooted, trashed and re-recreated the music library; rebooted the Homepods; rebooted the Airport Express; rebooted the Mac; but the problem persists. I've found other posts with similar issues (Airplay seems to be the common factor), but the only replies seem to be "update software". The software is fully up to date. Please note, this does not involve Apple Music or any other streaming service. It's simply trying to play files that are on my Mac via Airplay.

Any suggestions?