### Apache Airflow version

2.2.0b2 (beta snapshot)

### Operating System

Debian buster

### Versions of Apache Airflow Providers

_No response_

### Deployment

Astronomer

### Deployment details

Astro dev start

### What happened

"Already exists." error message is missing while updating user email with existing email id through API.

### What you expected to happen

"Email id already exists" error message should appear

### How to reproduce

1. Use a patch request with the below URL.
`{{url}}/users/{{username}}`
2. In payload use an exiting email id 
```
 {
        "username": "{{username}}",
        "password": "password1",
        "email": "{{exiting_email}}@example.com",
        "first_name": "{{$randomFirstName}}",
        "last_name": "{{$randomLastName}}",
        "roles":[{ "name": "Op"}]
}
```

### Anything else

_No response_

### Are you willing to submit PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

tests/api_connexion/endpoints/test_user_endpoint.py
autoclean_user_payload["first_name"] = "Changed"
        autoclean_user_payload["last_name"] = "Overlord"
        response = self.client.patch(
            f"/api/v1/users/{autoclean_username}?update_mask=first_name",
            json=autoclean_user_payload,
            environ_overrides={"REMOTE_USER": "test"},
        )
        assert response.status_code == 200, response.json
        
        data = response.json
        assert data["first_name"] == "Changed"
        assert data["last_name"] == "User"
    @pytest.mark.usefixtures("autoclean_admin_user")
    @unittest.mock.patch(
        "airflow.api_connexion.endpoints.user_endpoint.generate_password_hash",
        return_value="fake-hashed-pass",
    )
    def test_password_hashed(