feat(browse): sticky tabs + per-tab search bar (server-side, scope-aware)

The Browse tab nav scrolled away (operator didn't know it existed) and
Posts had no search. Roll the tab strip + a shared search field into one
sticky block pinned under the 64px TopNav.

- Posts gains server-side text search: PostFeedService.scroll()/around()
  + /api/posts accept q (ILIKE over post_title OR description), applied
  INSIDE the artist/platform WHERE so search stays scoped to the active
  filter. Scope shown as clearable chips next to the search field.
- Artists/Tags search consolidates into the sticky bar: their inner
  search boxes are removed; they react to route.query.q (q is deep-
  linkable, e.g. /browse?tab=posts&q=foo). Platform/kind filters stay.
- Posts empty state now distinguishes 'no matches' from 'no posts yet'.

Tests: posts q-search matches title|description and stays artist-scoped
(service); q passthrough (api).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

frontend/src/views/PostsView.vue

@@ -59,7 +59,8 @@
       </div>
 
       <div v-else-if="store.items.length === 0 && store.done" class="fc-posts__empty">
-        <p>No posts yet. Subscribe to a source on the
+        <p v-if="hasActiveFilter">No posts match your search or filters.</p>
+        <p v-else>No posts yet. Subscribe to a source on the
           <RouterLink to="/subscriptions">Subscriptions</RouterLink>
           tab to start capturing posts.
         </p>
@@ -93,10 +94,14 @@ const artistFilter = computed(() => {
   return raw == null ? null : Number(raw)
 })
 const platformFilter = computed(() => route.query.platform || null)
+const searchFilter = computed(() => route.query.q || null)
 const postIdFilter = computed(() => {
   const raw = route.query.post_id
   return raw == null ? null : Number(raw)
 })
+const hasActiveFilter = computed(() =>
+  artistFilter.value != null || platformFilter.value != null || searchFilter.value != null
+)
 
 // --- normal feed (downward infinite scroll) ---
 const sentinel = ref(null)
@@ -106,6 +111,7 @@ async function reload() {
   await store.loadInitial({
     artist_id: artistFilter.value,
     platform: platformFilter.value,
+    q: searchFilter.value,
   })
 }
 function onFilters({ artist_id, platform }) {
@@ -169,6 +175,7 @@ async function loadAroundAndAnchor() {
   await store.loadAround(postIdFilter.value, {
     artist_id: artistFilter.value,
     platform: platformFilter.value,
+    q: searchFilter.value,
   })
   await nextTick()
   const el = document.getElementById(`fc-post-${store.anchorId}`)
@@ -188,7 +195,7 @@ async function activate() {
 }
 
 watch(postIdFilter, activate)
-watch(() => [artistFilter.value, platformFilter.value], async () => {
+watch(() => [artistFilter.value, platformFilter.value, searchFilter.value], async () => {
   if (postIdFilter.value != null) return
   await reload()
   await nextTick()