How to connect HomePod to appletv

What is your model Apple TV? Identify your Apple TV model - Apple Support

Do you have the larger 6.8" HomePod (2018) or the smaller 3.3" HomePod Mini (2020)?

There is not auto setup on apple tv.

Sure there is, if already configured though the Home app.

Otherwise: Settings﹥Video and Audio﹥Default Audio Output﹥.

Set up home theater audio with HomePod and Apple TV 4K - Apple Support

There is no audio output option on Apple TV as well.

The connection is via the home network; Wi-Fi and/or ethernet.

Default audio output is a feature of Apple TV 4K. It is called Audio output on Apple TV HD (4th generation). Adjust other audio settings - Apple TV user guide - Apple Support

Apple TV HD (4th generation) doesn't allow to select HomePod as default speaker (at this time), only as temporary AirPlay speaker [1] [2].