Misleading authentication error during login for auth manager's with redirect auth flows

### Apache Airflow version Other Airflow 3 version (please specify below) ### If "Other Airflow 3 version" selected, which one? 3.1.7 ### What happened? We are using a custom auth manager implementation. When a client first accesses the web UI without having been authenticated, they see the "Error Unauthorized" landing page for about 1-2 seconds, before their authentication flow is completed. Since we are using a custom auth manager, we are not able to leverage recent fixes that were specifically scoped to the FAB auth manager (such as [this fix](https://github.com/apache/airflow/pull/61287/changes)). We are _not_ using the FAB auth manager, or any subclasses thereof, but the bug described here is similar in nature to the ones described in these 2 FAB auth manager issues: https://github.com/apache/airflow/issues/57981 https://github.com/apache/airflow/issues/55612 Our auth manager's `login` route handler initiates a sequence of redirects, which ultimately return to another route handler managed by our auth manager, which issues the Airflow access token from the user credentials issued from the redirect flow. TL;DR, the bug is as follows: 1. Unauthenticated client accesses the Airflow web UI at `base url` 2. Airflow core redirects the unauthenticated client to `/auth_mgr/login` 3. Route handler for `/auth_mgr/login` redirects client to internal auth flow, with an eventual callback to `/auth_mgr/airflow_token_from_creds` 4. `/auth_mgr/airflow_token_from_creds` handler sets the cookie and redirects the user to whatever their initial url was they requested in step 1. For the duration of steps 1-4, the "Error Unauthorized" landing page is displayed, but that page should not be appearing while the authN flow is in progress. ### What you think should happen instead? The "Error Unauthorized" landing page is displayed while a client is actively in the authentication flow, but that page should not be appearing while the authN flow is in progress. There should be some solutio…