feat(web): add SessionWatcher component for session management and handle session expiration

apps/web/lib/api.ts

@@ -10,6 +10,9 @@ async function apiFetch<T>(path: string, init?: RequestInit): Promise<T> {
     credentials: "include",
   });
   if (!res.ok) {
+    if (res.status === 401 && typeof window !== "undefined") {
+      window.dispatchEvent(new CustomEvent("session:expired"));
+    }
     const text = await res.text().catch(() => res.statusText);
     throw new Error(`API ${path} failed (${res.status}): ${text}`);
   }