No, it doesn’t mean that. (putting other security considerations aside for the moment)
Indeed, on the machine itself you would need the BW browser extension to handle passkey authentication. (BTW, that is expected for the desktop app as well, whenever it arrives.)
It seems with that restriction to your question it would be “impossible”. If you had your BW mobile app on your phone with you, you could scan the passkey login QR code (i.e. use cross-device authentication, which would need bluetooth on both ends, though). – Another possibility would be to use a separate hardware security key that stores the passkeys.