def METHOD_NAME(
    with_initial_bookmarks, consumer_async, mocker
) -> None:
    if with_initial_bookmarks:
        initial_bookmarks = ["db1:bm1", "db1:bm1", "db1:bm2", "db2:bm1"]
    else:
        initial_bookmarks = None
    mock_cls = mocker.MagicMock if consumer_async else mocker.Mock
    consumer = mock_cls()
    bmm = bookmark_manager(
        initial_bookmarks=initial_bookmarks,
        bookmarks_consumer=consumer
    )
    bookmarks_old = {"db1:bm1", "db3:bm1"}
    bookmarks_new = {"db1:bm4"}
    bmm.update_bookmarks(bookmarks_old, bookmarks_new)
    if consumer_async:
        consumer.assert_called_once()
        args = consumer.await_args.args
    else:
        consumer.assert_called_once()
        args = consumer.call_args.args
    assert len(args) == 1
    assert isinstance(args[0], Bookmarks)
    expected_bookmarks = (
        set(initial_bookmarks or []) - bookmarks_old | bookmarks_new
    )
    assert args[0].raw_values == expected_bookmarks