You need to polish first and remove all the oxidized paint then wax with a high quality synthetic wax.
Most paste wax is a “cleaner wax” that also contains a mild polishing compound which is why you are seeing paint transfer onto the pad. The polishing first will remove the oxidized paint that is causing that to happen. A true wax won’t remove oxidized paint unless there is a severe layer of it.
Also, a good wax needs the oxidized layer removed to properly adhere to the paint finish. Otherwise, it is adhering to the oxidized layer and comes off quickly in rain or during washing.