So this is interesting - if the wifi is causing issues, and especially if it happens on one wifi network and not another one - then it may help to "forget" the wifi network and then reconnect. It's possible that the wifi connection information has become corrupted, and the watch is constantly trying to connect, failing, then trying again and again and again, etc. "Forgetting" the network and reconnecting will reset that network connection.
To forget the network on your watch, go into settings and (while connected to the problem network) tap the network name, then tap forget. For good measure, do that on your phone too - go into the phone settings, wifi and tap the "info" "i" icon next to the network name, then tap "forget this network" .
Then - on your phone - tap that network to re-connect, re-enter your wifi password,, and see if the problem goes away.