Fix SSE route dependency and align architecture docs

frontend/src/contexts/useApp.ts

@@ -0,0 +1,11 @@
+import { useContext } from 'react';
+
+import { AppContext, type AppContextValue } from './app-context';
+
+export function useApp(): AppContextValue {
+  const context = useContext(AppContext);
+  if (!context) {
+    throw new Error('useApp must be used within an AppProvider');
+  }
+  return context;
+}