Apple Watch fitness workouts
I have downloaded workouts to my exercise library, but they aren’t showing up on my watch.
I don't understand the concept of downloading workouts, nor what you describe as the exercise library in Apple Watch.
All available workouts are already on the Watch or iphone.
Use the Workout app on your Apple Watch – Apple Support (UK)
If you meant Fitness + then the additional resource is at
How to use Apple Fitness+ – Apple Support (UK)
If you've gone through those and the issue is still not resolved, Contact Support.
Click here > Contact - Official Apple Support
or phone numbers
Click here > Contact Apple for support and service - Apple Support
and or Genius Bar Reservation and Apple Support Options - Apple