As I explained, I tend to think that iOS is at fault here because all apps that fail to cast do so through the same, system-wide error message.
By contrast, the 3 apps that cast flawlessly fail to do so with different, app-specific behaviors if I disconnect the Chromecast devices from the network.
Also, as I reported, the YouTube and MUBI apps used to cast flawlessly under iOS and until recent iOS updates.
Hence my conjecture that the failure to cast hast been introduced through recent iOS updates, perhaps the latest 16.6.
I cannot use AirPlay because my end points are Chromecast audio devices. I can cast to these devices flawlessly with an Android phone. This is what I do at the moment but it would be nice to be able to control these devices also with the iPhone.
I seem to remember that iOS 16 was supposed to provide better Chromecast support. This is not the case according to my experience, hopefully iOS 17 will improve.