Why don’t my Bose SoundTouch speakers show up in my Apple TV 4K’s AirPlay options?

I have two different Bose SoundTouch speakers which are both AirPlay 2 enabled, and both show up correctly as available AirPlay targets on my iOS and iPadOS devices.

However, neither show up in the AirPlay options of my Apple TV 4K (when I click the AirPlay button in the Control Center) — only “TV speakers” is displayed.

I assumed I could stream Apple Music on my Apple TV, and have the sound be played in multiple rooms in the house — am I missing something?

Note: I’ve already added both the Bose SoundTouch speakers as accessories in the “Home” app, and assigned them to the same room that the Apple TV is in,

to no avail.