Cleaning company does not dispose of the garbage - Should the company be sued?

How much money is it about? As I said, you can withhold it and I would do the same. No one sues over 500€, and for amounts like these, just to mention them casually, I wouldn’t need a lawyer either. But be aware that they will be even less willing to provide a warranty if it has to be claimed.

What does the disposal cost? Weigh lawyer and court costs against disposal. You have to bear and sue for the costs yourself at first.

the costs are rather manageable.
best you get a cost estimate and then deduct double that amount from the plasterer’s final invoice. at the same time, demand the contract-compliant completion of the work (cleaning up) with a set deadline, etc...

in Germany it’s quite simple: whoever wants money is the fool!
as long as you don’t pay, he has to front all the stuff to get his right (which he doesn’t even have). you don’t need a lawyer for that initially and it would be excessive.

How big is the "pile"? Maybe it's not even worth mentioning, on a normal construction site there should be a construction waste container anyway and possibly a mixed waste container, take matters into your own hands and clear everything away, unless you want to be right "at all costs".