Seems it's like ssh keys, but fiddled automatically in the browser. A password unlocks the local keys.
This means keys need to be transported between devices. Which means even tighter coupling to google and microsoft accounts.
This means keys need to be transported between devices. Which means even tighter coupling to google and microsoft accounts.
Pure keys are on tokens that support Bluetooth/NFC/USB to talk to whatever devices you want. One can use a built in key on a device with a security enclave which means using one device to auth addition of another, but you might do that with alerts to authorize, etc.
Anyone who doesn't have a powned problem is using something like TOTP auth codes which has all of the downside of Fido and none of the convenience.
A site that doesn't want you to could try to use attestation certificates to force you to use a real vendor's keys which should never be extractable.
EDIT: Yes you don't need to use a syncing service. But it will be important for it to be portable between syncing services, as that is what most consumers will be using.