Audio is not sent to Marshall Bluetooth headphones

I'm having trouble using my Marshall Monitor II headphones with my new iPhone 16 (no problems whatsoever with my previous iPhone). What happens is I can connect to the headphones via Bluetooth, but the audio still plays through the iPhone speakers (I tried with several different apps). If go into AirPlay in the Music app the headphones are not listed there. The headphones are listed and connected in the Marshall Bluetooth app (I can control the ANC from there, for example), but the audio controls are greyed out. Any ideas what may be the problem?