I mean: 2fa-code, login, password instead of: login, password, 2fa-code. Maybe login could be automatically filled based on 2fa-code public key? That should prevent leaking password to fake page.
A cheap Security Key has no idea what public key it told you to use when registering.
There's a cute trick here. When you tell a key "Hi, authenticate please" you must send it a "cookie" it gave you during registration. Now this could in theory be some pointer it uses or whatever. But in fact it's actually the private key it will use to authenticate, encrypted with its own baked in secret key. It decrypts that, then authenticates. But if you don't know which user you're authenticating you can't send their cookies, you'd have to try every cookie for every user. Not fast.
If every user uses WebAuthn then just a login (username or email address or something) is enough. But if some just have passwords then doing anything before the password step gives away what's up.
An interesting solution could be to first enter the username, then the OTP/Key, then the password. I haven't given it a lot of thought and can't find anything wrong with it.
Like GP said, that would give away which accounts have WebAuthn enabled on them, since those without it would send you straight to the password prompt instead.
But more importantly, phishing sites will always tell you 'your key succeeded. Enter your password next' regardless, so this doesn't protect against password disclosure at all.
Nope, because you'd be relying on the fraudulent phishing page to tell you that.
Real page: Give me login
You: Login
Real page: Good login, press your 2fa to authenticate
You: Press
Real page: Good 2fa, enter your password
You: Password
Versus:
Fake page: Give me your login
You: Login
Fake page: Good login, press your 2fa to authenticate
You: Press
Real page: Good 2fa (wink wink), enter your password
You: Password
The fake page wouldn't have a working login to the real page because the 2fa would be wrong, but it would still have your password.
I mean: 2fa-code, login, password instead of: login, password, 2fa-code. Maybe login could be automatically filled based on 2fa-code public key? That should prevent leaking password to fake page.