Sorry for not being clear.
Once I paired my watch with my phone, it (the watch) automatically "inherited" any wifi network to which the phone connected. I tested this in a few locations by (a) switching off Bluetooth on the phone and (b) walking out of BT range of the phone. In each case, the watch retained wifi access as long as it was on the same wifi network. That's how Apple says it should work
Your experience seems to be that the watch will only "get" the wifi network if it's with the phone while the phone is establishing a connection for the first time. That's anomalous, and not as documented. If it works, then at least it enables you to use the ufcntionality and it's certainly something that people should try.
Clearly the phone must pass credentials to the watch, for the watch to have direct access to wifi (which it must for Siri, for example, to work without the watch). It makes sens that forgetting/reconnecting to a newtork would triugger the phone/watch to exchange the new credentials - it's just not supposed to be necessary.
I hope that makse more sense than my last effort