I was describing my experience on iOS 15 for the past year or so.

The incorrect results I'm seeing are in-app—what do you mean that it's not fully integrated in iOS 15?

Prior to iOS 16, Apple Weather was using 'The Weather Company' for their forecasts I believe.

Yep. I’m on ios15 and it says “weather channel” at the bottom

There's a brand new Weather app in iOS 16. It's (more or less) the same functionality as Dark Sky was.