emulator can't generate auth/account-exists-with-different-credential error

Operating System

macOS

Browser Version

Safari 16.5.2

Firebase SDK Version

10.1.0

Firebase SDK Product:

Auth

Describe your project's tooling

index.html with source tag.

Describe the problem

The Firebase Auth Emulator can't generate the auth/account-exists-with-different-credential error.

Steps and code to reproduce issue

The following code generates the aforementioned error without using the emulator.

const githubProvider = new GithubAuthProvider();
const googleProvider = new GoogleAuthProvider();

try {
    await signInWithPopup(auth, githubProvider);
    await signInWithPopup(auth, googleProvider);
    await signInWithPopup(auth, githubProvider);
    console.log("signed in successfully...oops.");
} catch (error) {
   console.error(error);
   if (error.code === 'auth/account-exists-with-different-credential') {
       console.log("untrusted->trusted->untrusted");
   }
}

This page explains that the error should be thrown, because I am signing in to an untrusted provider, then to a trusted, and then to the same untrusted one, using the same email in the whole process. And indeed, the error happens without the emulator. However, with it I am able to sign in successfully and instead the user gets 2 providers

firebase / firebase-tools