How to control sound on TV/monitor via Apple TV?

I have run into a stupid problem and I do not know, how to solve it. I am hoping some in here might be able to help me.

I have purchased a computer monitor together with an Apple TV. I thought it would work together as a "TV" - I was looking for a 32" TV-solution in 4K in my summerhouse and hence the wish for a "small" TV.

I thought the Apple TV could control the audio. It turns out it cannot as the monitor does not accept IR-signal. How do I go about this problem?

I have tried to find an "IR USB-stick", but that does not seem to exist. Then I have thought about adding a soundbar, but would that work, if the monitor just has HDMI and no ARC? 

Would the HomePod solve the problem? Would that be controlled directly from the Apple TV?

If I could get a Roon Ready soundbar I could solve another problem and would be tempting.

Any help would be much appreciated. Thanks a ton in advance.