firebase-auth updateUser with providerToLink using "password" as providerId

Hey I'm trying to link providerData with providerId = "password" using firebase admin SDK

environment :

• Firebase SDK version: 10.0.2
• Firebase Product: auth
• Node.js version: 16.13.0
• NPM version: 8.1.0

The problem
I'm trying to link providerData using firebase admin SDK in order to link providerData with providerId = "password" .
I'm using updateUser method and pass providerToLink object in order to link providerData.
updateUser method will return this error :

• code : auth/invalid-provider-id
• message : The providerId must be a valid supported provider identifier string.

Relevant Code:

await admin
            .auth()
            .updateUser(user.uid, {
                providerToLink: {
                    uid: user.email,
                    email: user.email,
                    displayName: user.displayName,
                    providerId: 'password',
                },
            })
            .catch((error: any) => {
                console.error(`${error}`);
            });

Start at admin.auth().updateUser and its providerToLink handling, then trace validation of providerId="password". Reproduce the report with the stated SDK and Node.js versions and check the Firebase Auth API contract; done means the behavior is clarified or corrected and covered by focused validation.