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

alembic/versions/0005_note_search.py

@@ -0,0 +1,33 @@
+"""notes full-text search vector
+
+Revision ID: 0005
+Revises: 0004
+Create Date: 2026-07-20
+
+A generated tsvector column (title weight A, body weight B) + GIN index, so
+search is index-backed and always in sync with the row (no trigger to maintain).
+"""
+from alembic import op
+
+revision = "0005"
+down_revision = "0004"
+branch_labels = None
+depends_on = None
+
+
+def upgrade() -> None:
+    op.execute(
+        """
+        ALTER TABLE notes ADD COLUMN search_vector tsvector
+        GENERATED ALWAYS AS (
+            setweight(to_tsvector('english', coalesce(title, '')), 'A') ||
+            setweight(to_tsvector('english', coalesce(body, '')), 'B')
+        ) STORED
+        """
+    )
+    op.execute("CREATE INDEX ix_notes_search ON notes USING GIN (search_vector)")
+
+
+def downgrade() -> None:
+    op.execute("DROP INDEX IF EXISTS ix_notes_search")
+    op.execute("ALTER TABLE notes DROP COLUMN IF EXISTS search_vector")