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/components/AppShell.vue

@@ -1,5 +1,5 @@
 <script setup lang="ts">
-import { computed, onMounted, ref } from "vue";
+import { computed, onMounted, ref, watch } from "vue";
 import { useRoute, useRouter } from "vue-router";
 import { useSessionStore } from "../stores/session";
 import { useConfigStore } from "../stores/config";
@@ -14,6 +14,8 @@ const config = useConfigStore();
 const labels = useLabelsStore();
 
 const managing = ref(false);
+const searchText = ref(typeof route.query.q === "string" ? route.query.q : "");
+let searchTimer: ReturnType<typeof setTimeout> | undefined;
 
 onMounted(() => {
   if (!labels.loaded) void labels.load();
@@ -21,6 +23,24 @@ onMounted(() => {
 
 const currentLabelId = computed(() => (route.name === "label" ? String(route.params.id) : null));
 
+function onSearch(value: string) {
+  searchText.value = value;
+  clearTimeout(searchTimer);
+  searchTimer = setTimeout(() => {
+    const q = searchText.value.trim();
+    if (q) router.push({ name: "search", query: { q } });
+    else if (route.name === "search") router.push("/");
+  }, 250);
+}
+
+// Clear the search box when navigating to a non-search view.
+watch(
+  () => route.name,
+  (name) => {
+    if (name !== "search") searchText.value = "";
+  },
+);
+
 async function signOut() {
   await session.logout();
   await router.replace("/login");
@@ -32,15 +52,27 @@ async function signOut() {
     <header
       class="sticky top-0 z-20 border-b border-neutral-200 bg-neutral-50/90 backdrop-blur dark:border-neutral-800 dark:bg-neutral-950/90"
     >
-      <div class="flex items-center justify-between gap-4 px-4 py-3">
-        <div class="flex items-center gap-2">
+      <div class="flex items-center gap-3 px-4 py-3">
+        <div class="flex shrink-0 items-center gap-2">
           <div class="flex h-8 w-8 items-center justify-center rounded-lg bg-brand text-sm font-black text-neutral-900">
             TS
           </div>
           <span class="hidden font-semibold sm:inline">{{ config.siteName }}</span>
         </div>
-        <div class="flex items-center gap-3">
-          <span class="hidden text-sm text-neutral-500 sm:inline dark:text-neutral-400">{{
+
+        <div class="flex flex-1 justify-center">
+          <input
+            :value="searchText"
+            type="search"
+            placeholder="Search notes…"
+            aria-label="Search notes"
+            class="w-full max-w-md rounded-lg border border-neutral-300 bg-white px-3 py-1.5 text-sm outline-none focus-visible:ring-2 focus-visible:ring-brand dark:border-neutral-700 dark:bg-neutral-900"
+            @input="onSearch(($event.target as HTMLInputElement).value)"
+          />
+        </div>
+
+        <div class="flex shrink-0 items-center gap-3">
+          <span class="hidden text-sm text-neutral-500 md:inline dark:text-neutral-400">{{
             session.user?.display_name
           }}</span>
           <RouterLink
@@ -98,7 +130,7 @@ async function signOut() {
         </nav>
       </aside>
 
-      <main class="min-w-0 flex-1"><slot /></main>
+      <main class="min-w-0 flex-1"><RouterView /></main>
     </div>
 
     <LabelsModal v-if="managing" @close="managing = false" />