Passkey is some sort of specific unique key to a device allowing to use a pin on a device instead of the password. But which won't work on another device.
Now I don't know if that key can be stolen or not, or if it's really more secure or not, as people have really unsecure pins.
Yes, but that's missing the important part.
Passkeys is not primarily about asymmetric keys. It's about applying asymmetric keys to the Web as an open standard.
The W3C Web-Authn standard is what makes it important and revolutionary.
This is just as important as HTML, CSS and ActivityPub.
Finally we have an open standard that integrates in the web and offers a high level of security.
Is that like TLS client-side certificates?
It's actually quite similar, yes, in the sense that it uses a public/private key pair linked to your account.
But this works on the application layer and you don't use certificates.
Much easier to setup.
Also it generates unique keys per site so it doesn't help anybody track you