Part of the design is that every site will support multiple passkeys tied to an individual account. So it will be normal to use one browser to bootstrap registering another browser with a new passkey into your account. This video[1] by the FIDO alliance shows what that process will look like with a bunch of different OS and browser combos.

[1]: https://www.youtube.com/watch?v=SWocv4BhCNg

I would assume so, but I'm not 100% sure. I personally haven't yet messed with Passkeys much aside from use on a couple of sites that have implemented them.

My working assumption is if you wanted to use a new browser, you'd have to attempt to log into the service with the new browser. When the Passkey flow prompts you with a QR code to scan, you'd have to use your iPhone/iPad to scan that QR code to allow entry. What happens after that, I have no clue.

The keys aren’t stored in the browser. The browser just forwards to the hardware.

Switching from one password/-key manager to another is going to be more of an issue.

But you should be able to add an additional passkey once logged in to an account, just like how you can have multiple hardware 2fa keys now. Then you could manually migrate accounts that way, which is painful, of course, but you wouldn’t be completely locked in.