What is the function of the zener diodes used in this setup?

zener diodes (or diodes in general) only conducts current in one direction

That is only partly true, Zener diodes will also conduct when the reverse voltage exceeds a certain value. Here that value is 2.4 V (they are 2.4 V zeners). Add to that the forward voltage of the other Zener (about 0.7 V) and the two Zeners in series will start to conduct when the voltage across both exceeds 3.1 V. When that voltage is negative (-3.1 V) the same will happen.

These diodes limit the input voltage difference to the opamp. Too much voltage difference will destroy the opamp.

zener diodes ... only conducts current in one direction.

On the contrary, the defining behaviour of Zener diodes is that they conduct in both directions, albeit with different forward voltages. That is, forward biased, they typically behave like a regular silicon diode, and have a forward voltage of ~0.7 V. However, when reverse biased, they have a well defined breakdown voltage (2.4 V in your schematic above), and a reverse bias above their breakdown voltage causes current to flow.

Therefore, if the voltage across the D3/D4 pair exceeds approximately ±3.1 V (2.4 V + 0.7 V), they will "clamp" and prevent the voltage from increasing further. So yes, this acts as a transient voltage suppression technique.