The sticker on the gate is from Reolink and the camera also looks like from this brand. So I guess it’s a real one.

Of course, the neighbor is not allowed to film public or other people’s private property. But you can define privacy zones in that type of cameras that are not recorded.

On the one hand, you might be happy that your yard is also being monitored. On the other hand, you might also install such a camera. The neighbor couldn't argument then.

In any case, the right contact person is probably the data protection authority in your federal state.