HomePod Minis Airplay with Both Audio and Video

We have a pair of HomePod Minis paired with each other for stereo. We also have an Apple TV. Though most of our viewing occurs on platforms within the Apple TV, sometimes we watch live sports that are only available via other platforms, like ESPN+.

When doing so, we can start streaming the content on one of our iPhones and then use AirPlay to “cast” it on the TV so that we can watch on a much bigger screen. However, we can’t seem to get audio output from the HomePod Minis simultaneously with the video. If I start streaming on the phone and then swipe down to get to the Control Center, I can click the small AirPlay icon, and I can select both the Apple TV and HomePod Minis, as if they’re bundled together, like this:

But this results in audio output from the HomePod Minis with no video being cast to the TV.

Curiously, both of them appear selected here, though:

If I click on Control Other Speakers & TVs, then it looks like the speakers are connected but the Apple TV isn’t:

So am I doing something wrong or is it not possible to stream video and audio via AirPlay in this way?