Playback thru Apple TV - but not with Audacity?

I have my MacMini set up to playback audio via an Apple TV to my HiFi. This works fine with iTunes - alt/click on the speaker icon (MacOS toolbar, top right of screen) and select Apple TV instead of Headphones as the Output Device
However, when I try this with Audacity, it stays locked onto the Headphone Output. Alt-click on the speaker icon shows Apple TV selected but the sound still comes through the headphone output. I can save a project and then play it back thru iTunes but I’d like to be able to play from Audacity straight to the Apple TV/HiFi
Have I missed a setting here?

The Audacity setting can be different from the machine setting. Use the Audacity Device Toolbar to set the destination.

All the available devices should be listed there. If they’re not, that’s a different problem.