This is an extremely reproducible condition, across multiple watch models and iPhone models, all running latest software versions (as of 27.Feb.24).
When the paired phone is on the same wifi network as the watch, the weather complication shows null data (dashes and blanks). Turn off wifi on the paired phone, and the complication works, loading weather data accurately.
Turn on wifi on the phone again, and the weather complication stops updating and you are unable to see any weather data for other locations.
Because this is so consistent and predictable, Apple should be able to diagnose and implement a fix in an upcoming OS update (either phone or watch, or both).
I also wonder if this is the cause of excessive battery drain since updating the watch to WatchOS 10? Perhaps related to watch unable to update the weather complication while phone is on wifi?