Well, turns out I should have caught up a bit earlier on this new-fangled e-invoice thing, because, as it turns out, handing an invoice into the federal state of Baden-Württemberg (and probably the others these days, too) requires formatting it as a nice, sleek, validated e-invoice.
So. There I am. Fortunately I am using a lovely book-keeping programme that is able to whip up such invoices. Not so fortunately is that it is Neuland, as Germans would say, to me and I have to figure out all the bits and pieces that have to go in there (and are still missing).
It's on the way, though. And then at least I'll know more about this stuff, because it will probably not be the last thing I deliver to some public or state institution. At least I hope so!