After you changed the Wi-Fi password on your router, the Apple TV would notice that by getting disconnected.
Settings﹥Network﹥Wi-Fi﹥Not Connected
Trying to re-connect to the same network name (SSID) would result in a failed try, followed by an endless spinner.
After a restart, then choosing
Settings﹥Network﹥Wi-Fi﹥Not Connected﹥Other…
You would be asked for the network name. Enter it.
It would try to connect with the memorized password, but fail again. Then it will ask for a new password. Enter it.
You are now connected.
- Apple could make some UX improvements here. Changing the password is not that rare.
- This could be avoided by changing the network name/SSID too. (One character difference is enough.) But that might get awkward if the old network name is used again in the future, when users forgot this happened, and why.
- This could be avoided by having Apple TV forget the network before changing the password.