Can the Speedlite 430EX III-RT be triggered by a third party RF trigger, and does it require a separate receiver to do it?
The 430EX III-RT has a built-in Canon RT radio transceiver, so it does not need a separate receiver on its foot to be remotely triggered/controlled. It only needs you to have a compatible transmitter on your camera hotshoe. And there are a number of 3rd-party transmitters that are RT compatible that are not the Canon ST-E3-RT.
The Jinbei TR-Q7 (aka the Westcott FJ-X2m), Yongnuo YN-E3-RT, or Phottix Laso transmitters should all work.