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

src/thoughtsync/notes.py

@@ -4,7 +4,7 @@ import uuid
 from datetime import datetime, timezone
 
 from quart import Blueprint, g, jsonify, request
-from sqlalchemy import delete, select
+from sqlalchemy import delete, func, literal_column, select
 
 from .acl import visible_to_user
 from .auth import login_required
@@ -93,6 +93,36 @@ async def list_notes():
         return jsonify({"notes": out})
 
 
+@bp.get("/search")
+@login_required
+async def search_notes():
+    q = (request.args.get("q") or "").strip()
+    if not q:
+        return jsonify({"notes": []})
+    async with session_scope() as db:
+        tsquery = func.websearch_to_tsquery("english", q)
+        # search_vector is a generated column (migration 0005), not mapped on the ORM.
+        search_col = literal_column("notes.search_vector")
+        stmt = (
+            select(Note)
+            .where(
+                visible_to_user("note", Note.owner_id, Note.id, g.user_id),
+                Note.deleted_at.is_(None),
+                search_col.op("@@")(tsquery),
+            )
+            .order_by(func.ts_rank(search_col, tsquery).desc(), Note.updated_at.desc())
+            .limit(100)
+        )
+        notes = (await db.scalars(stmt)).all()
+        labels_map = await _labels_for_notes(db, [n.id for n in notes])
+        out = []
+        for n in notes:
+            data = n.serialize()
+            data["labels"] = labels_map.get(n.id, [])
+            out.append(data)
+        return jsonify({"notes": out})
+
+
 @bp.post("")
 @login_required
 async def create_note():