Where does this app get its weather info from? The National weather service, or a private Corp. such as Accu Weather?

Prior to iOS 16, Apple got its ten-day forecasts from the Weather Channel. With iOS 16 and later, the data originates from the enigmatical Apple Weather. See Feature availability and data sources in the Weather app - Apple Support

See also: Check the weather on iPhone - Apple Support

Since I don't care for Apple's inaccurate weather, I added the free U.S. National Weather service web app on my iPhone 14 Pro Max (iOS 16.6) and pointed it at the NWS reporting site that is 5-miles distant at the local airport. That is my source of accurate weather.

All the data sources for the Weather App are listed in the support document you posted from.

Was that not clear enough?

Do you need further information to that?