refactor: simplify OAuth routes, add type safety, deduplicate UI components

- Extract handleOAuthCallback to eliminate GET/POST duplication in oauth.ts
- Add P2002 race condition handling in findOrCreateUser
- Add .unref() to stateStore cleanup timer to not block process exit
- Use Provider union type instead of bare strings throughout OAuth code
- Export API_BASE from api.ts, reuse in OAuthButtons
- Extract MobileBranding component to deduplicate Login/Register mobile brand
- Extract shared Logo component in AuthBranding
- Remove unnecessary WHAT comments

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

packages/web/src/lib/api.ts

@@ -1,4 +1,4 @@
-const API_BASE = '/api';
+export const API_BASE = '/api';
 
 type ApiResponse<T> = {
   success: boolean;