M2 search: Postgres FTS backend + top search bar + results

- Migration 0005: generated tsvector column (title A + body B) + GIN index on
  notes; GET /api/notes/search?q= (websearch_to_tsquery, ts_rank, ACL-scoped,
  excludes trash), labels merged into results.
- Persistent AppShell layout (parent route + <RouterView> children) so the new
  top search box keeps focus across board/search/label navigation.
- SearchView (debounced live search from the shell → /search?q=, results masonry,
  no-match empty state); BoardView/SearchView render inside the shared shell.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01FRgehjoz7Yv8LkUfADxACm

frontend/src/router/index.ts

@@ -6,28 +6,17 @@ const router = createRouter({
   history: createWebHistory(),
   routes: [
     {
+      // Persistent authed shell (sidebar + top bar + search); children render in it.
       path: "/",
-      name: "board",
-      component: () => import("../views/BoardView.vue"),
-      meta: { requiresAuth: true },
-    },
-    {
-      path: "/archive",
-      name: "archive",
-      component: () => import("../views/BoardView.vue"),
-      meta: { requiresAuth: true },
-    },
-    {
-      path: "/trash",
-      name: "trash",
-      component: () => import("../views/BoardView.vue"),
-      meta: { requiresAuth: true },
-    },
-    {
-      path: "/label/:id",
-      name: "label",
-      component: () => import("../views/BoardView.vue"),
+      component: () => import("../components/AppShell.vue"),
       meta: { requiresAuth: true },
+      children: [
+        { path: "", name: "board", component: () => import("../views/BoardView.vue") },
+        { path: "archive", name: "archive", component: () => import("../views/BoardView.vue") },
+        { path: "trash", name: "trash", component: () => import("../views/BoardView.vue") },
+        { path: "label/:id", name: "label", component: () => import("../views/BoardView.vue") },
+        { path: "search", name: "search", component: () => import("../views/SearchView.vue") },
+      ],
     },
     {
       path: "/settings",
@@ -63,8 +52,6 @@ router.beforeEach(async (to) => {
   if (to.meta.requiresAdmin && !session.user?.is_admin) {
     return { name: "board" };
   }
-  // Registration closed: keep people out of the register screen (the very first
-  // account is still creatable because allow_registration defaults to true).
   if (to.name === "register" && !config.allowRegistration) {
     return { name: "login" };
   }