The grout is not anthracite but partially gray?

Sorry, but the grout lines are clearly different in their color

Yes, you are right. But the tiles also seem to be two different ones: the second photo has a different color temperature and is also better saturated. Therefore, the grout lines must also look comparably different – and thus you cannot compare photo 1 with photo 2.

The tiles are different.

Are the tiles actually different or do the pictures deceive? Were the tiles installed in more than one room?

The tiles are the same, unfortunately the recordings were made under different lighting conditions - therefore the grout lines also appear different.

Have the same problem. Grout mortar or its pigments did not distribute evenly. There’s nothing to do except a grout refresher. That will happen with us in January. It looks just like in the pictures of the OP, only much more "patchy". Unfortunately, the refresher will make everything darker (we wanted lighter grout) but the surface should at least be uniform and consistent then.

Good evening, what is a "Fugenrefresher"?

I would like to have dark, uniform joints.

Do you have a product recommendation for me?