Passkeys, under the hood, use a way of proving your identity that doesn't require you to actually send your password, and also doesn't require you to send your username either.
Because of how it's implemented, the system managing the passkeys also gets to authenticate that the website is who it says it is.

So no private data actually gets sent anywhere, but you can prove your identity while also checking the identity of the site you're talking to, like the SSL lock icon but automated. It's often implemented such that the device that holds they keys can't actually have them stolen from it, and it's integrated with a biometric sensor.
This means it's possible to have a high degree of confidence that the person logging in is physically the same person who created the credential, and not just someone who had their password stolen.

The final perk, is that if you're using something like a phone with a fingerprint scanner, passkeys work as two factors of authentication, despite only feeling like one.
Because the phone verifies your identity via fingerprint (something you are), it can then unlock the key that is uniquely available to the phone (something you have).

Combine that with being generally easier to use, and it's pretty clear why most security experts are pushing them. Security that users will use is better than security they won't, and finally we have easier to use security that's also better than the more difficult options.