No. I find it easiest to keep this straight in my head with a line from the U2 song "The Fly", "a secret is something you tell one other person". You're thinking of Ed25519 private keys, you mustn't tell those to anybody and they're minted as a pair with a public key you can tell to everybody.
> What's to prevent me from using a similarly long, randomly generated secret as my password
That's a Shared Secret. You tell the password to the remote web site. They have a copy of it, their permanent copy of it is likely hashed, but you send them a new, unhashed version of that same password to the site every single time you log in.
This makes all the difference in the world. Let's see that in action:
Suppose that Edward, who is Evil, has complete insight into everything stored by and every program running at Facebook for an hour. If someone logs into Facebook using a password, obviously Edward learns the password, it was sent to Facebook so they could check it was correct. So Edward can log in as any Facebook user who logged in while Edward's magical insight lasted? Right?
Nope. Facebook has WebAuthn. For WebAuthn users logging in involves public key cryptography. Facebook has a public key for those users but no private key. Edward can see that the users were properly authenticated, but he doesn't get a persistent credential because the persistent credential never left the user's grasp. He cannot log in as those users, only they can do that.