fix: reduce excessive POST /api/auto-mode/context-exists requests

Two changes:
1. Server: Skip morgan logging for context-exists endpoint (like health check)
2. UI: Use a stable fingerprint (feature IDs + statuses) instead of the
   unstable features array reference as the useEffect dependency. This
   prevents re-checking context for all features on every React Query
   refetch when the actual feature set hasn't changed.

apps/server/src/index.ts

@@ -261,7 +261,10 @@ morgan.token('status-colored', (_req, res) => {
 app.use(
   morgan(':method :url :status-colored', {
     // Skip when request logging is disabled or for health check endpoints
-    skip: (req) => !requestLoggingEnabled || req.url === '/api/health',
+    skip: (req) =>
+      !requestLoggingEnabled ||
+      req.url === '/api/health' ||
+      req.url === '/api/auto-mode/context-exists',
   })
 );
 // CORS configuration