Next time use more compact format for yours picture. I think some people just don't want to lost their valuable points to see your picture.
For example GIF or PNG format. I convert your circuit into GIF format.
You are right. It is push-pull amplifier. But I didn't see any overcurrent protection.
Besides push-pull amplifier output current is limited itself by push-pull principle.
The most of transistors just biased current sources.
Simulation can help understand it in full detail, but you need to know sizes of transistors and resistors value.
As I understand NMOS M21, M10, R3, C1 and M21 and the similar mirrored PMOS components are DC negative feedback that help bias M29 and M30 to limit quiescent current. But this this feedback can reduce AC gain also. So this feedback suppressed for AC signal by C1. I.e. for AC signal this negative feedback doesn't work.
Another thing. I think the current of all mirrors is too low (because all this currents are included in quiescent current). The mirror current is not enough to control the gate of M29 or M30 efficiently. So there is another positive feedback that help to increase a slew rate of the gate signals of M29 and M30:
M21, R7, M22 and M28 (with mirrored PMOS component).
That's my idea at first glance.
I hope it help you.