feat: add groups to search vector

Co-authored-by: Cursor <cursoragent@cursor.com>

docs/groups-architecture.md

@@ -975,9 +975,11 @@ Each functional unit can be implemented as a **separate issue**:
 ### Issue 5: Search Integration
 **Type:** Backend  
 **Estimation:** 2h  
+**Status:** ✅ Implemented (migration `20260217120000_add_group_names_to_member_search_vector.exs`, Issue #375)
+
 **Tasks:**
 - Update search vector trigger to include group names
-- Extend fuzzy search to search group names
+- Extend fuzzy search to search group names (via search_vector; no Elixir change needed)
 - Test search functionality
 
 **Acceptance Criteria:**