Drill an additional inlet in the rainwater inlet box?

oh yes, good point! I was somehow so focused on providing something at the outlet.

I also looked yesterday regarding a T-piece under the sink tank. The water is directed there into a KG pipe.
But I couldn't find any T-pieces/branches with DN 75 for KG pipes. Did I search poorly or do they really not exist? For the path from the carport, I wanted to use a DN75 HT pipe. How do you connect the two now?

PS: Sorry, I think it's obvious that we outsourced the outdoor facilities.

Do you mean a 100/75 branch? Those exist. For my part, I laid a DN100 KG2000 for the terrace roof and then made a 100/75 reduction to the drain there. KG2000 is a bit more expensive than HT, but more robust. You can lay it accordingly without sand bedding.

Are you referring to a 100/75 branch? Those exist.

But only with HT pipes, right? With reductions, apparently the same. I could then do it like you. T-piece on the KG pipe and KG pipe leading to the carport with the same diameter. Then put an HT reduction from 110 to 75 on there. That should probably work, even if I would have quite a bit of work with the adjustments on the KG pipe.
Have you ever seen something like this in use?:

It is placed on the existing pipe, cutout marked, cutout removed, and then the branch glued on with a (special?) adhesive. In the narrow eaves edge, that would of course be optimal, maybe even the only option.