When I hit the back button on my Apple TV 4K remote, the unit shuts off

Assuming this is a new issue after you've been using your ATV4K successfully in the past (IOW, you're familiar with using the device), I suspect the remote's gone temporarily funky.

The ATV4K's Siri Remotes are known to just go flakey on rare occassions, and they need to be fully reset and then re-paired to the ATV4K device. I suggest you jump straight to the last procedure in this Apple support doc: If your Siri Remote or Apple TV Remote isn't working - Apple Support. It's a quick process that can't hurt anything.

Cool. Glad that did it. You're welcome.

Please do us a favor and mark my advice as the solution to your issue. That'll make it easier for folks to find in searches should they suffer the same :-).