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/lib/nav.ts

@@ -0,0 +1,29 @@
+/* The left-nav map: one entry per section, each its own route/page. This is the single
+ * source of truth shared by the sidebar (which renders the links) and the auth frame
+ * (which seeds the store's active section from the URL on first load). Runs is the root. */
+import type { Section } from "@/components/store";
+
+export interface NavRoute {
+  key: Section;
+  href: string;
+  label: string;
+}
+
+export const NAV_ROUTES: NavRoute[] = [
+  { key: "runs", href: "/", label: "Runs" },
+  { key: "repositories", href: "/repositories", label: "Repositories" },
+  { key: "agents", href: "/agents", label: "Agents" },
+  { key: "schedules", href: "/schedules", label: "Schedules" },
+  { key: "approvals", href: "/approvals", label: "Approvals" },
+  { key: "servers", href: "/servers", label: "Git Servers" },
+  { key: "activity", href: "/activity", label: "Activity" },
+  { key: "shared", href: "/shared", label: "Shared" },
+  { key: "login", href: "/login", label: "Claude Login" },
+];
+
+/* Map a browser path back to its section key. Trailing slashes (Next emits them under
+ * `trailingSlash: true`) are normalized away; anything unrecognized falls back to Runs. */
+export function sectionFromPath(pathname: string): Section {
+  const clean = pathname.replace(/\/+$/, "") || "/";
+  return NAV_ROUTES.find((r) => r.href === clean)?.key ?? "runs";
+}