Could you be in Theater mode? This setting turns on Silent Mode, and the screen stays dark until you tap or press a button. See:
Use Control Center on your Apple Watch - Apple Support
If that is not the problem, the first (and simplest) thing to try if something isn’t working right is to restart your Apple Watch and its paired iPhone. If necessary (device not responding), try a forced restart. Both methods can be found here:
How to restart your Apple Watch - Apple Support
Restart your iPhone - Apple Support
If that doesn't help, the next steps would be to unpair and pair your watch again and restore from the backup. This deletes all temp and corrupted files and re-indexes the file system.
Unpair and erase your Apple Watch - Apple Support
Set up your Apple Watch - Apple Support