Accidental damage is not covered by your limited warranty.
A damaged screen cannot be repaired - only replaced. While screen replacement will be expensive, it may be appreciably less expensive than replacing the iPad.
You can check availability/eligibility for repair - and associated cost for your country/region - here:
iPad Repair & Service - Apple Support
In addition to Apple's mail-in repair service, you can arrange repair at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP):
Genius Bar Reservation and Apple Support Options - Apple
Many users of iPad prefer to avoid potential screen damage by installing a Screen Protector before damage occurs. A Screen Protector is typically made of very thin tempered/toughened glass, or plastic film.
Your iPad screen is the single most expensive component of your iPad - whereas a screen protector is sacrificial layer that, if damaged, is easy and relatively cheap to replace. While adding a Screen Protector won't repair existing damage to a screen. However, the adhesive layer can, in some circumstances, fill or significantly reduce visibility of very minor scratches or blemishes.
Zagg and OtterBox are amongst the better manufacturers of tempered glass screen protectors - with good reputation. Always choose a screen protector from a well known brand - choosing a screen protector that is specifically designed for your iPad model.
Good quality tempered glass screen protectors from reputable manufacturers, that are designed for your iPad, will have absolutely no impact upon sensitivity of the screen or usability of an Apple Pencil. By contrast, cheap “generic” screen protectors of any type, whether glass or film, can cause problems. The good options often include a money back guarantee.
Of available options, Zagg arguably have the best reputation; you are very unlikely to find reported issues or complaint with their screen protector products.