DIAGNOSIS This is usually a conflict with your router's settings, specifically the wireless channel or band steering. The Apple TV 4K (3rd gen) can be picky about congested Wi-Fi channels.
FIX Start on the Apple TV. Go to Settings > Network. Select your Wi-Fi network and choose 'Forget This Network.' Restart your router—unplug it for 30 seconds. Once the router is back online, go back to the Apple TV Network settings and rejoin your Wi-Fi, entering the password carefully. This forces a clean connection.
IF THAT DIDN'T WORK The issue might be your router using a Wi-Fi channel the Apple TV doesn't like. Log into your router's admin page (usually via a web browser) and try two things: 1) If you have a dual-band network (2.4GHz and 5GHz), temporarily disable the 2.4GHz band and connect the Apple TV to the 5GHz band only. 2) Manually set your 5GHz channel to a lower one, like 36, 40, 44, or 48.
HEADS UP For a permanent fix, consider using an Ethernet adapter. The USB-C port on this model supports Apple's Ethernet adapter, which gives you a rock-solid connection and is worth it if your TV is near your router.