Is any readback required when ATC uses the phrase "RADAR CONTACT"? As the title says, is a readback required? I've heard some people say that it's not required, while some others say we should readback our call sign only. Some even say just push the transmission knob twice to inform the controller that we are acknowledging.

Which one is the correct action and what are the references or publications?
No. It is an information by the controller to let you know that you have been heard &amp; identified. As he doesn't pass any relevant or critical information, there is no need to readback.
The same goes with e.g. wind information given by ATC.