feat: add groups to search vector

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

test/mv_web/member_live/index_groups_integration_test.exs

@@ -8,6 +8,7 @@ defmodule MvWeb.MemberLive.IndexGroupsIntegrationTest do
   - Groups sorting works with other sortings
   - Groups work with Membership Fee Status filter
   - Groups work with existing search (but not testing search integration itself)
+  - Member index search by group name returns members in that group (Issue #375)
   """
   # async: false to prevent PostgreSQL deadlocks when creating members and groups
   use MvWeb.ConnCase, async: false
@@ -212,6 +213,25 @@ defmodule MvWeb.MemberLive.IndexGroupsIntegrationTest do
     # (that's part of Issue #5 - Search Integration)
   end
 
+  test "member index search by group name returns members in that group", %{
+    conn: conn,
+    member1: member1,
+    member2: member2,
+    group1: group1
+  } do
+    # member1 is in group1 "Board Members", member2 is not
+    conn = conn_with_oidc_user(conn)
+    {:ok, view, _html} = live(conn, "/members")
+
+    view
+    |> element("form[phx-submit='search']")
+    |> render_submit(%{"query" => group1.name})
+
+    html = render(view)
+    assert html =~ member1.first_name
+    refute html =~ member2.first_name
+  end
+
   test "all filters and sortings work together", %{
     conn: conn,
     member1: member1,