A very strange problem.
When I run the APK directly from Android Studio, the content observer in question fires as expected. When I use Build APK to create a debug APK, download it to a phone and install via Package Installer, everything is OK.
But when I create a signed release, and install this APK using Package Installer, the content observer will not fire.
The content observer in question is content://mms/
Tested this with targetSdkVersion and compileSdkVersion of Android 9 (API 28) and Android 10 (API 29). The Android devices were all Android 11.
The app works fine in every other way (there are many other features, all of these work).
EDIT: When I use Build APK to create a debug APK, download it to a phone and install via Package Installer, everything is OK.
** I was unable to replicate the above subsequently i.e. debug APK working correctly. **