I want to plan by writing on real paper or a tablet, because that's when I can think best, but I want the output to be computer text, so it's easy to share, copy and search by everyone. Is there anything that comes close to this and is actually good?

Lars recommends remarkable.com and says he may have a voucher to get you some €85 off or so. If you're interested you should drop him an email. (DM me if you've forgotten his address)

I bet it's good but from the looks of it, the handwriting recognition so leaves a lot to be desired. Why do these tools completely ignore dithering like underlines, headers etc.? My dream tool would detect formatting and allow to export markdown.

That would be amazing, for sure. Sadly such a tool is indeed probably called a secretary.

I wonder if it would be ridiculous to hire an assistant... :D