The network test on the device will not show an accurate representation. You would just to run a diagnostic report for the network. Use istumbler (Mac), netstumbler (PC) or similar. This will give accurate values for signal strength, noise, and also show nearby networks.
Make sure DNS on Apple TV is set to auto (settings - general - network)
If on wifi you can try ethernet
The issue will resolve around the network, so it would be better to consult your ISP if you'd rather not investigate yourself.
You would be using an older model Apple TV, which doesn't run apps. Those are preset 'channels' which are sent via server. When it is unable to connect to the network those icons will disappear. Be aware that if it were a second gen that is classified as obsolete and no longer supported. If issues persist it may be hardware related and that model is almost 10 years old.
Identify your Apple TV model - Apple Support