I don't have the immediate texts at hand but I cite sources in my guide about taking time off in Germany. The law is very unambiguous about what vacations are for. A nice example is that if you get sick during your vacation, it counts as sick days and you can use your vacation days at a later time.

https://allaboutberlin.com/guides/vacation-days

My guides about sick leave and sabbaticals just add a bit of context. Sick days are really well protected.