I revisited the basics of Physics and while studying work done, I came across the following question:

You stand on roller skates facing a wall. You push against the wall and you move away. Discuss whether the force exerted by the wall on you performed any work.

This question is from my school textbook and the answer is as follows:

No work was done because there is no displacement. You moved but the point where the force is applied never moved.

I don't understand why this is the case. Of course, the force I applied on the wall has not done any work because the wall is not moving, but the reaction force from the wall, that is, the force that the wall has applied on me has led to motion.

So shouldn't we apply the formula $W=Fs\cos\theta$ to find the work done by the wall on me?