Wie schafft es Tokio, dass man dort anders als in NYC fast nie Ratten sieht?

It is estimated that there are around 3 million rats in NYC and about 0.3 million in Tokyo. This is a difference with factor 10.

By the way, Kuala Lumpur is extremely and should have almost twice as many rats as New York. But it is clear that such estimates are anything but accurate. But on the spot you see them all the time.

Returning to your question that the rat population in Tokyo is so much smaller, can actually be only two things; either the habitat is less suitable for the rats, or 10 times worse than in NYC. Or the rats are more active. Something that seems to me personally that in cities like New York or even Kuala Lumpur or Taipei, which have a real rat problem, there are always plenty of garbage out there for a long time. And that makes Tokyo better than now, for example, New York. But garbage bags & open garbage cans provide not only an optimal food basis for rats, but they also lead the rats to run more actively through the streets to search for food and are more visible to people than if they live, for example, only in the sewer and also search for their food there.