It would be great if you still had some interviews scheduled before you accepted the current position. In this case just wouldn't mention you have already started a new job.

If you decide to start searching a new position within the first 2 months after starting the current I wouldn't mention that you are currently working if I were you.

Otherwise just say the truth - that you like your current tasks but the culture is different to what you expected. Be prepared to answer very precise questions concerning that however. I'm currently looking for a new job after spending 2/3 of a year in a horrible work culture and I'm still treated with suspicion. Germany is very conservative when it comes to that.

Also during job interviews with new companies, try to frame it more as "I want to work for you" and not as "I don't want to work for my current company".