Apple Watch is not user-serviceable and Apple does not offer a screen repair or screen replacement service.
There is no also user setting for touchscreen sensitivity.
Unless Apple instructs otherwise, to interact with Apple Watch, tap on the screen rather than pressing firmly on it.
If your Apple Watch does not respond to touchscreen inputs and other interactions as expected, then the following steps may help:
Remove any screen protector, case or bumper that you may have fitted to your Apple Watch.
Clean your Apple Watch, including the Digital Crown, being sure to follow Apple's cleaning instructions:
Restart (normally) your Apple Watch and iPhone, turning both devices off together, then restarting your iPhone first:
If the issue persists, next unpair and re-pair your Apple Watch:
If the issue then still persists, I suggest that you contact Apple Support (remote diagnostics and/or mail-in service may be available, if required), make a Genius Bar reservation or visit an Apple Authorised Service Provider for assistance: