Password is necessary for two-factor authentication. The factors of authentication are something you know (like a password), something you have (like a cell phone), and something you are (like a biometric).
An example of three-factor authentication would be this—imagine a spy going into a secret bunker. They need to scan their iris, insert a key card, and then enter a passcode before the door opens. This has all three factors of authentication; the passcode is something they know, the key card is something they have, the iris scan is something they are.
If it just sends a code to your phone, that’s one-factor authentication (something you have). Anyone with your phone can get into your account. Unless, of course, your phone hides its notifications and you have a screen lock. Then that’s actually two-factor authentication because you also need to know the phone PIN or have the biometric.
If it just asks for a password, that’s one-factor authentication (something you know).
If it asks for your password and then sends a code to your phone, which you need a fingerprint or face scan to unlock, you have achieved three-factor authentication.
Edit: Interesting tidbit—in the USA, you can rent a mailbox at the post office to receive mail when you don’t want to give out your real address. Useful for privacy reasons. I’m sure they have similar things in other countries. These mailboxes come with a key. This is actually two-factor authentication, because the keys usually don’t have the mailbox number written on them! So you have to have the key and also have to know which mailbox among the hundreds at the post office it opens.
Okay bud. Have a biscuit 🍪