Unable to switch to bluetooth headset

I am using a Pixel 6 Pro with the latest OTA updates. I’m also using Deezer beta version 7.0.23.1. My bluetooth headset is WH-1000XM3.

Here are the steps to reproduce:

• Connect the headset and play something in Deezer. Audio comes out of the headset as it should. All is normal.
• Open the “Audio output” panel at the bottom during playback and switch to the PC client using “Deezer connect” → “your PC”
• Now go back to the “Audio output” menu. You’ll see “Bluetooth” below “My phone”. Select “Bluetooth” and this makes the Android system bluetooth menu appear. If you select the bluetooth headset from that menu, nothing happens. Music continues to come out of the phone speakers instead of the bluetooth speakers.

I’m not able to figure out how to get this working. Am I missing something? At the moment, I’m trying out Deezer in a trial to see if I want to stick with it or go back to Spotify. So far, I’ve seen 2 bugs related to the Android app that are discouraging (this one, if it is a bug, and another related to being unable to control Deezer playing on PC from Android which was fixed in Android beta 7.0.23.