I am experiencing the exact same problem on Apple TV 4 gen. I haven’t been able to access the App Store for the past 2-3 days. I contacted Apple support on Twitter and but they were not very helpful:
“We'd like to get this headed in the right direction so you can get back to enjoying your Apple TV. For this issue, please reach out to our Apple TV Advisors. You can reach them using our link here: http://apple.co/GetSupport”