Fix UI not updating after first login on cold start

[iaromoskviak]

Fixes a cold-start timing issue where login succeeded but the UI did not update until a manual refresh.

On initial load, auth and privilege state were not propagated reactively, causing the header and privilege-based menus to render as unauthenticated. This was due to late auth subscriptions, non-replayed auth events, and privilege checks throwing during initialization.

Fixes:

1. Fetching privileges immediately after successful login
2. Make privilege loading non-throwing on cold start
3. Subscribe to auth state early and recompute privileges reactively
4. Using BehaviorSubject for auth to support late subscribers
5. Simplifying getAuth() to expose a stable auth stream