I figured out my problem using the approach I intended. Now I can handle user authentication using an external API that returns a JWT (access token) upon successful authentication. The login Razor page of my Blazor WebApp project (in auto-rendering mode) is a static SSR page. The authentication state is then transferred to the interactive rendering mode using the new Blazor 9.0 APIs: AddAuthenticationStateSerialization() and AddAuthenticationStateDeserialization().
Here is my solution as a minimal repo, which demonstrates how these features can be implemented.