Pandora actually launched its official Apple Watch app back in January of last year. The app supported offline playback, but it did not support the ability to stream music and/or podcasts from the app without having an iPhone connected. That is changing today, though.
Pandora has updated its official app (via MacRumors) to support streaming without the requirement of a connected iPhone:
Introducing our new standalone Apple Watch app!
Leave the phone at home and bring all of your listening with you thanks to our updated Apple Watch app. Now you can stream your favorite music and podcasts, straight from your wrist – no phone required.
To get the app, you can either upgrade your current iOS app if you already have it installed. Or you can also install the standalone Apple Watch app from the App Store on the smartwatch, which was made available with the public launch of watchOS 6.