How Do i Fix Light Scratches?

For an answer to screen durability, I trust JerryRigEverything to show us what's what. Sadly, the Nintendo Switch's screen is made from Plastic, and is much more apt to scratching than a phone screen made of glass. Repairing scratched plastic is nigh impossible, and some of the methods you listed (toothpaste, nail polish remover) will likely do more harm than good.

If your device is under warranty, you may be in luck on getting the screen replaced, and it's worth reaching out to Nintento's customer support to confirm.

If you're feeling plucky, you can always attempt to replace the screen on your own, using replacement parts and a guide from a reputable source like iFixit. Otherwise, you may just need to bite the bullet, put a tempered glass screen protector on it to prevent further damage, and hope that your brain can ignore the scratch.