Coder plugin: Fallback authentication button still appears after user has already authenticated

Issue comes from a customer – moving an anonymized version here for more visibility.

## Problem
When the Coder plugin is integrated into a Backstage deployment, authentication doesn't always work as expected. The authentication elements don't appear/disappear consistently, and interacting with an element that does not exist sometimes causes the deployment to blow up.

## Steps to reproduce
1. Add the `CoderProvider` and `CoderWorkspacesCard` components to a deployment
2. Navigate to whichever page has the card and authenticate via its built-in UI
3. Navigate to a different page.
4. See that the fallback "Authenticate with Coder" button is present at the bottom of the screen, even though the user should already be authenticated
5. Click the button – the application blows up