Both, currently; notably it's mostly not what goes to your local grid, but rather mostly to the larger scale grid. It's about a 60/40 to 70/30 split between production/"grid-usage-fee" ("Netznutzungsentgelt").

It basically pays off the grid stability provision bids for fast-response power, and the transmission itself.

It'd likely be helpful if the peak part could be regulated in a way that's more condusive to match the actual impact you create on transformer sizing, not the worst-case impact you might have. Because there's a difference between a mostly-uncorrelated peak of shower+cooking vs. the car+cold day, because your neighbours don't shower the same time, but the several hours of charging do often overlap and the cold is the same across a neighbourhood that shares a local substation.

But yeah, for the most part, transformer size isn't that large of a contributor to overall electricity provision expenses, so I don't expect that to be a significant problem by that 2027 law.