The first sidebar was actually requested by Huggbees, and the hosts would keep the tradition going over later episodes when appropriate.
In most occasions, the gag is that the hosts will not actually exit the Discord call, yet still have a private conversation anyway. They will jokingly "complain" about the guest's performance in a supposedly secretive manner.
Often the guest will chime in, themselves being in on the gag, to point out that they can still hear the hosts. At this point, the hosts will feign awkwardness and resume the episode proper.