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Upvote:2
Istanbul airport provides free tours for those with 6-24 hour layovers, which appears to include you. The info page for the tour points to a Turkish government page which says that Germans do not need a visa for stays of up to 90 days.
I had two 4-hour layovers in that airport and while the lounge was nice, I kind of had my nose pressed up against the glass wishing I could go out and see the city. Take the free tour, it should be fun!