if your phone is in bluetooth range, the wifi on the watch should already be powered down, that toggle will just prevent it from turning on if you move away your phone. If your phone is close, then getting network over bluetooth from the phone uses less battery than wifi
try rebooting your phone and your watch for starts.
no response on all your devices usually is sorted by a reboot of home-hubs (aTV and homepods), sometimes a router reboot can help too. But if the home app is working fine on your other devices, it's probably not the issue here.