Yes, we do have an Apple Watch app!
The app is supported by Series 3 and onward, and requires watchOS 7 or newer.
You'll only be able to view the cook on your watch, so setups and adjustments will still need to be done in the app on your iPhone. But if you have mobile data enabled on your Apple Watch, you'll be able to leave your phone at home, then monitor the cook on your watch from anywhere!