Selecting the audio output to Bluetooth when connected to AV adapter (HDMI) into a mini projector

I am trying to direct the audio to play on a pair of bluetooth speakers while my iphone 8 Plus is connected via the AV adapter to a mini projector.

Connector:

https://www.apple.com/shop/product/MD826AM/A/lightning-digital-av-adapter?fnode=6b56c8d0f6e0c9d7e5e75c92eb103996dabd616f1a7d57795816c83ae7eba6e26e622ab22160b51516e86002c6629759653c96a8c76c3afd123a5b85164e88e998cc98976f347d1b098f865f3aaaf205774081474ad92cde59d828436fba72af

I have tried selecting the Speaker (Wonderboom 2) through the AirPlay settings but then the video (the source is Netflix playing on my iphone) will play on my phone and not through the projector. The audio will play from the bluetooth speaker. The projector will still be mirrored but it will freeze and video continues playing on the iphone. Has anyone successfully set this up?