I wrote a primer about sick days here: https://allaboutberlin.com/guides/sick-leave

15 is the average. I use it to reassure people that it's okay to take sick days, and not one of those rights that no one dares to use.

Usually, employers ask for a doctors' note after 3 consecutive sick days, but the reason for the sickness remains hidden from the employer. The note just gives a time range, nothing more.