As already said in the first video they are doing an Retraction / Extension Test only with the use of the Yellow Elec Pump and no Ground Cart. Thus the PTU needs to operate to pressurize the Green System which is in use for Retraction / Extension.

If i have a Ground Cart available i would avoid the use of only the Elec Pump / PTU because, as you can see, they are able to do the Job but having a hard time. Personally i would like to have a smother operation. But there is nothing wrong doing it only with the Elec Pump.

In the second Video, during operation of the LDG Gear there is a very high demand in the Green Hydraulic System. Big Actuators needs to move a lot of weight simultaneously. This leads to an pressure drop in the Green System which in turn will trigger the Threshold Limit and the PTU starts to Operate. Perfectly normal situation. There is no Logic in the A320 which will turn on the PTU automatically during LDG Operation. It's just because of the pressure difference between G and Y during high demand operation.

In the A330 e.g. you have a logic which will turn on the Elec Pumo during LDG Operation to "support" the EDPs.

Been flying an airplane where you can hear the PTU sound constantly, but there’s no indication in the cockpit. Wonder what’s going on
left it written on the tech log.