The HomePod doesn't need to be the source of the audio to control the AppleTV. You just need to be specific with your directions.
"Hey Siri pause the living room AppleTV" will stop my AppleTV 4K in the living room. Since its the only device in the living room that accepts HomeKit play/pause commands than I don't need to add on "AppleTV" (its name in home app). So tell the HomePod "Hey Siri pause the living room" works too. HomePod Siri will respond with "stopping in the living room", "resuming in the living room", etc.
Since the HomePod is for music and a speaker it will fill gaps in your commands with its own functions so you need to just be aware of that. "Hey Siri pause" will be met with "Nothing is playing". You need to say "Hey Siri pause (location) (device)".
There are plenty of other commands that work from the HomePod to control the AppleTV when its being used for video. I often use "Hey Siri rewind X seconds/minutes in the living room" when I get distracted in the kitchen or something.
It should be mentioned this is not a function of the HomePod. This is a function of HomeKit. These are commands that work on any device that accepts Siri commands, iPhones, iPads, Macs (not mine so not sure about Macs), Apple Watch, AppleTV. Often the HomePod doesn't pick up my Hey Siri command for the AppleTV but my iPhone, Apple Watch or iPad (when plugged in) does and it executes the same command the HomePod would have just fine. That is another reason specifics are important with you're commands.
You can even use the AppleTV's Siri remote to control OTHER AppleTV's (ex. from the living room AppleTV remote "Pause guest bedroom AppleTV 4") albeit function is limited its still there.