Check for a second page of messages without counting the room

The original room shows its welcome box until it holds more than a page of
messages, and paged? answered that with a COUNT(*) over every message in
the room on each visit. Asking whether there is a row past the first page
answers the same question while reading at most a page of index entries.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NuTtwJKhb77Dv7EQqv2C3C

app/models/message/pagination.rb

@@ -49,7 +49,7 @@ module Message::Pagination
     end
 
     def paged?
-      count > PAGE_SIZE
+      offset(PAGE_SIZE).exists?
     end
   end
 end

test/models/message_test.rb

@@ -65,6 +65,18 @@ class MessageTest < ActiveSupport::TestCase
     assert_equal room.messages.ordered.first(Message::Pagination::PAGE_SIZE).map(&:id), room.messages.first_page.map(&:id)
   end
 
+  test "paged? tells whether a room has more than a page of messages without counting them all" do
+    room = Rooms::Closed.create!(name: "Paging", creator: users(:david))
+    Message.insert_all Array.new(Message::Pagination::PAGE_SIZE) { |i| { room_id: room.id, creator_id: users(:david).id, client_message_id: "paging-#{i}" } }
+
+    assert_no_queries_match(/COUNT/i) do
+      assert_not room.messages.paged?
+
+      Message.insert_all [ { room_id: room.id, creator_id: users(:david).id, client_message_id: "paging-next" } ]
+      assert room.messages.paged?
+    end
+  end
+
   private
     def create_new_message_in(room)
       room.messages.create!(creator: users(:jason), body: "Hello", client_message_id: "123")