Split the web UI into a page per section

The dashboard was a single route that swapped section components via a
`section` state field. Convert it to the App Router's multi-page model so
each left-nav selection is its own route (/, /repositories, /agents,
/schedules, /approvals, /servers, /activity, /shared, /login), making the
pages modular and independently updatable.

- Move the token gate + store provider + sidebar into a persistent frame
  (AppFrame + Shell) rendered by the root layout, so auth, the polling
  loop, and shared state survive client-side navigation.
- Sidebar items are now <Link> routes; the active item and the store's
  polled section are derived from the URL (lib/nav).
- Each section gets an app/<section>/page.tsx; Runs stays at root and keeps
  its full-height split layout, the rest render in the shared scroll frame.
- Emit per-route index.html (trailingSlash) so the FastAPI StaticFiles
  mount serves clean slash-terminated URLs with no SPA rewrite.
- Regenerate the bundled static export.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01PsAeGVadULRzPhV2PRDttM

frontend/components/store.tsx

@@ -189,17 +189,22 @@ export function useDashboard(): StoreValue {
 export function DashboardProvider({
   token,
   onUnauthorized,
+  initialSection = "runs",
   children,
 }: {
   token: string;
   onUnauthorized: () => void;
+  /* Which section is on screen at mount, derived from the URL by the auth frame. The
+   * provider lives in the root layout and mounts once, so this only seeds the first
+   * poll; later navigation updates the section through setSection. */
+  initialSection?: Section;
   children: ReactNode;
 }) {
   const client = useMemo(() => createClient(token, onUnauthorized), [token, onUnauthorized]);
   const clientRef = useRef(client);
   clientRef.current = client;
 
-  const [section, setSectionRaw] = useState<Section>("runs");
+  const [section, setSectionRaw] = useState<Section>(initialSection);
   const [projects, setProjects] = useState<Project[]>([]);
   const [agents, setAgents] = useState<RunAgent[]>([]);
   const [selectedProjectId, setSelectedProjectId] = useState<string>("");