TLDR;
watchOS app is displayed an iOS app, be it a standalone watchOS app or a watchOS app with an iOS app companion.
So go to TestFlight on the iOS device that's paired with the Apple Watch device.
Find the app you want to test.
Go to the detail page, and see "Show App on Apple Watch" option on the last list of App Information.
You have to run watchOS version that is compatible with your target app in Xcode, otherwise the menu will be disabled.
I'm currently on a mission to master watcOS app development and stumbled upon this very problem. This is my learning:
Make sure you understand the concept of standalone watchOS app and watchOS app with iOS app companion.
Make sure your Apple Watch test device is paired with yout iPhone test device.