To the OP
I believe this is how it works with WhatsApp.
If you leave your phone at home , you’ll still receive WhatsApp messages & reply the normal way. For this the phone needs to be switched on.
If you leave your phone at home & switch your phone off , you will not receive WhatsApp messages at all on your watch. Once the phone is switched on they come through , prob on phone though before your watch.
As others have said , there’s no native WhatsApp watch app & prob never likely to be the rate WhatsApp updates things.
WatchChat is good , but like a lot of 3rd party apps , it has its limitations. Worth a punt though.
Cheers.