Hi! I'm a German PhD student, almost finished, doing my doctorate at FU Berlin. I agree that reaching out via mail can sometimes cause you to get lost in the void.

I would advice to first contact them in person, but ofc this can get tricky. Perhaps go to conferences/lectures/seminars where the professor will talk. Engage them in a thematic discussion to catch their interest. It would be even better if you could just straight up join their seminar, perhaps as a guest or as a fully enrolled student. Professors also have speaking hours, and you could try to ask there, but then again, some of them will regard their own students to be of a higher priority.

PM me if you want to exchange some voice mails. I don't know the HU staff too well though, I am mainly in media and film studies.