Can I just implore you to read the Apple site on Passkeys I linked above? Feels like there’s a lot of things you’re misunderstanding and it would help if you understood the whole idea before coming up with these questions.
Here is the link again:
https://developer.apple.com/passkeys/
The standard was created by FIDO, not Apple, and it was built to use a key pair per site, no one would use one key pair (meaning a private key and a public key) for all sites. A private key only corresponds to one public key so it’s not possible to reuse one private key with many public keys or vice-versa. This is called asymmetric cryptography.
The private key stays on device, and it gets backed up to iCloud (or potentially a local backup if you still plug it into a Mac or PC and do manual backups, I haven’t heard if they enabled that but maybe). It also syncs all your passkeys with other iCloud devices you’ve signed into (well, running iOS 16 at least since presumably passkeys won’t be supported on earlier iOS versions). And you absolutely can still use passkeys after restoring from a backup, or if you have another device it will sync back from that device, say if you lost your iPhone but your iPad or Mac is still available you can get a new iPhone and it will sync your passkeys to your new iPhone. This is all covered on the Apple site I linked.
The big problem will be if you have no backups whatsoever and you have one Apple device. You are a bad fit for Passkeys then, if you ever lose said device. But if you have 2 Apple devices they sync passkeys, or if you have 1 and you enable iCloud backups you will have no problem with losing Passkeys.
Getting a public key is meaningless, it doesn’t help a hacker whatsoever, you don’t need the public key for anything (it’s used to generate a challenge that the private key responds to and if the response is correct because the private key was used it‘s authenticated) and it doesn’t reveal anything about the private key.
Apple tightly controls how passkeys (private keys) can be shared, besides iCloud syncing and backup they only share passkeys over Airdrop. They demonstrated this in a developer focused video. Otherwise you will have no option to get at the private key because it’s secured along with other system data.
Apple does not have access to your passkeys. The passkeys are indeed backed up to iCloud, however the backups are encrypted and Apple can’t access them, this is also described in the link.