Each phone or computer you sign in on needs a passkey of its own, unless your passkeys are shared through iCloud Keychain or Google Password Manager.

1. On a device you are signed in on, open a site's Settings.
2. Under People and agents, press Sign in on another device beside your name.
3. Open the link it makes on the other phone or computer, and save a passkey there.

The link works once, for two weeks, and the passkey it saves signs in to every site you look after.