Yes, calling window.location.reload() should be sufficient in your case to restart the login flow. When the page reloads, Auth0 will handle the authentication process again and generate a new authentication transaction state.
Auth0 is designed to handle these scenarios seamlessly. When the page is reloaded, Auth0 will recognize that the authentication transaction has expired and initiate a new login flow. The new login flow will generate new values for the URL query parameters, including the state parameter.
By using window.location.reload(), you ensure that the user is redirected back to the appropriate initiate_login_url for their specific app/client. This eliminates the need for branching logic to determine the client_id and redirect accordingly.
Overall, this approach should work well and provide a better user experience by warning users and giving them the option to restart the login flow when the session has expired.