Just an addendum - I thought perhaps I hadn't waited long enough, but I still get the same type of error the next day. I had added weather kit capability via +Capability in Xcode. I checked Certificates, Identifiers & Profiles in developer.apple.com, and it shows a checkmark next to WeatherKit for both the original iOS app as well as the new watch target.
I also created a completely new project containing a new watch app with associated iOS app and again added the WeatherKit capability for both targets in Xcode, and get the same type of errors. I am now also getting some errors that say "Info.plist contained no UIScene configuration dictionary (looking for configuration named "(no name)")", but the app "runs" and I can get location, etc... just not weather.
Just in case the problem is that adding the WeatherKit capability in Xcode isn't "good enough", I deleted the capability in the new project in Xcode, deleted the AppID in Certificates, Identifiers & Profiles, then recreated the AppID in Certificates, Identifiers & Profiles with the bundle ID already shown in Xcode, and with WeatherKit checked during AppID creation. This resulted in the exact same errors.