So what does speedtest say? The behavior you're describing is consistent with the ATV4k not being close enough to the access point. 5GHz has less reach than 2.4GHz so it's common for it not to connect at a distance where 2.4GHz already is weak.The apple tv is more frustrating than anything I owned till now !
The internet does not work on 5ghz channel. And on the 2.4 , frequently notice buffering and today it randomly disconnects and a restart only helps. This has been going on for more than an hour, and in the same time no other device has this issue.
Speedtest is the most used on my Apple TV !
If you can pull an ethernet cable that'd be the best, cheapest and fastest. If you do that maybe get a cheap 8-port gigabit switch that you can put in your media center to connect other devices.