feat(search): align conversation search order

internal/repository/search_repo.go

@@ -199,9 +199,9 @@ func (r *SearchRepo) searchConversationsInternal(ctx context.Context, accountID
 
 	// Apply sort + pagination
 	orderClause := filter.OrderClause()
-	// Conversations default to last_activity_at DESC NULLS LAST
+	// Chatwoot SearchService#filter_conversations orders by created_at DESC.
 	if filter.SortBy == "created_at" || filter.SortBy == "" {
-		orderClause = "conversations.last_activity_at DESC NULLS LAST, conversations.id DESC"
+		orderClause = "conversations.created_at DESC, conversations.id DESC"
 	}
 
 	err := q.Offset(filter.Offset()).Limit(filter.PerPage).

internal/repository/search_repo_test.go

@@ -362,6 +362,29 @@ func TestSearchRepo_SearchConversations_DoesNotMatchLabelsOrMessages(t *testing.
 	assert.Empty(t, results)
 }
 
+func TestSearchRepo_SearchConversations_DefaultOrderUsesCreatedAt(t *testing.T) {
+	db := setupTestDB(t)
+	repo := NewSearchRepo(db)
+
+	account := createTestAccountForSearch(t, db)
+	older := createTestConversationForSearch(t, db, account.ID, "open", "")
+	newer := createTestConversationForSearch(t, db, account.ID, "open", "")
+	base := time.Date(2026, 6, 7, 12, 0, 0, 0, time.UTC)
+	olderActivity := base.Add(time.Hour).Unix()
+	newerActivity := base.Add(-time.Hour).Unix()
+	require.NoError(t, db.Model(older).Updates(map[string]any{"created_at": base.Add(-time.Hour), "last_activity_at": olderActivity}).Error)
+	require.NoError(t, db.Model(newer).Updates(map[string]any{"created_at": base.Add(time.Hour), "last_activity_at": newerActivity}).Error)
+
+	filter := &search.SearchFilter{Page: 1, PerPage: 25}
+	results, total, err := repo.SearchConversations(context.Background(), account.ID, "", filter)
+
+	require.NoError(t, err)
+	assert.Equal(t, int64(2), total)
+	require.Len(t, results, 2)
+	assert.Equal(t, newer.ID, results[0].ID)
+	assert.Equal(t, older.ID, results[1].ID)
+}
+
 func TestSearchRepo_SearchConversations_WithStatusFilter(t *testing.T) {
 	skipIfSQLite(t)
 	db := setupTestDB(t)