Hi,
no need to worry.
without load (picture1) the waveform seems like a pure square wave. But it is driven: 41% high side / 9% OFF / 41% low side / 9% OFF. (estimated %)
One can not recognize the 2 x 9% OFF time.
During OFF there is stored energy in the core of the transformer. This causes the voltage to go to the opposite side of the last driven polarity.
Since there is no load (current) there is no power and there is enough energy to keep voltage level high (negative or positive; far away from zero)
On picture2 and 3 there is load. And the waveform during dead time (fast rising to the opposite voltage, then fast step back and then medium fast rising) is a combination of the transformer´s stored energy and the inductances CMNF1 and CT:1.
The slowly falling top is caused by the increasing current and the decreasing voltage of the input capacitors.
How did you measure picture4? With a current probe?
Klaus