Passkeys are effectively software security keys, stored in whatever keychain you're using (Chrome or iCloud Keychain or otherwise); for the major implementations you're hearing about, the goal of their implementation is improving the UX by syncing your passkeys between devices, so as long as you can access your passkey keychain, you won't have to worry about losing your security key for that website.

As for how "passwordless" plays into this, Passkeys are generally better than passwords simply because it's PGP instead of a shared secret you send to the website, so even if a website is compromised, there's effectively 0 way the compromised database will enable password stuffing attacks on other websites.

Another cool thing is QR codes via caBLE (cloud assisted BLE), you can scan a QR code on a browser (on a bluetooth-enabled computer) to have your phone connect to that computer and present its passkey to the computer, without needing to actually plug in your device to the computer. This is not strictly a passkey thing, it just aids in making them usable.