Building construction is a legal trade in Germany. There are a lot of illegal immigrants working on that trade too. Maybe the relation is more to do with the "booming" economy.

> Literally dozens of thousands of them. Citation needed.

> increasing demand for prostitution by the order of magnitude A whole magnitude? Citation really needed.

In Germany a john has to report to the police if he suspects the prostitute is being coerced, if there are legal women, why would he seek an illegal one and risk jail time?