That could happen for the legacy models (A1469 or earlier), but shouldn’t happen for the 4K models (A1842 or later), as the latter have their apps downloaded on their disk.
What is the exact model?
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support
When the legacy models do not have a functional internet connection, they would show just Settings and Computers, as all the other app icons are loaded from the internet (Apple servers). Then the solution would be to set up the home network connection again (Wi-Fi or ethernet). It would remember previously used SSID network names and passwords, but if at least part of that has changed, then it wouldn’t be able to connect without manual assistance.