HDMI Splitter and HomePod Audio for Apple TV, Xbox, and Switch

I have been trying to get all my devices to play audio through my HomePod. All three are connected to a HDMI splitter so that I only need to run one cable to the TV. The Apple TV works, of course, but the other two (Xbox and Switch) don't work. I am currently hooked up to my Samsungs eArc HDMI input and I have it activated in the TV's software, I also have it turned on in the Apple TV's software. Those two work perfect together (4K HDR (HDR+) and Atoms Audio. Do I need to run the Apple TV into the eARC HDMI input on the Samsung and then, using a splitter, run the gaming consoles into the other available HDMI input? If I do that will I be able to hear the gaming consoles on the HomePod? Thanks for any advice.

[Re-Titled by Moderator]