Why do some cards not have numbers on them (e.g. Apple Card)?

Newer fintech credit cards don’t always have card numbers on them.

Does this really add security? How would I register my card to my wallet then?

Many cards these days operate entirely on the chip mechanism which is considered more secure and robust than the mag-strip, and not having your number on the card generally does make it safer but not by much as there is a difference between your account number and the number on your credit card

The biggest reason for this is that numbers are no longer needed for a card to function. Years ago, those numbers would appear on a slip of paper for customers to sign, but now many cards operate entirely on the chip mechanism, providing a safer and better experience.

The prime reason is that most of the card nowadays operates on the chip mechanism rather than the mag-strip, making it a safer experience.