Apple TV won’t let me select sound bar

If your soundbar is connected to your TV,

Apple TV →[HDMI]→ TV →[HDMI eARC/ARC]→ soundbar

then select “TV Speakers” as Audio Output, and set your TV for audio passthrough to the soundbar. That sends the audio signal over HDMI as you would want.

That makes no difference. It is still a TV setting.

Apple TV →[HDMI]→ TV →[optical]→ soundbar