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>

backend/app/api/posts.py

@@ -17,6 +17,7 @@ async def list_posts():
     cursor = args.get("cursor") or None
     artist_id_raw = args.get("artist_id")
     platform = args.get("platform") or None
+    q = (args.get("q") or "").strip() or None
     limit_raw = args.get("limit", "24")
     direction = args.get("direction", "older")
     around_raw = args.get("around")
@@ -56,7 +57,7 @@ async def list_posts():
         if around_id is not None:
             result = await svc.around(
                 post_id=around_id, artist_id=artist_id,
-                platform=platform, limit=limit,
+                platform=platform, q=q, limit=limit,
             )
             if result is None:
                 return _bad("not_found", status=404, detail=f"post id={around_id}")
@@ -64,7 +65,7 @@ async def list_posts():
         try:
             page = await svc.scroll(
                 cursor=cursor, artist_id=artist_id,
-                platform=platform, limit=limit, direction=direction,
+                platform=platform, q=q, limit=limit, direction=direction,
             )
         except ValueError as exc:
             # Service raises ValueError for malformed cursors only;