Is it allowed to position privacy screens arbitrarily on your own property?

Different laws apply to parking spaces (carports/garage). And mostly within the building envelope. Border construction is allowed there. But you should know that if you are building/have built.

As far as I know, setback distances must be observed for sheds and the like.

That is not the case everywhere. At least in Brandenburg, you are allowed to place garages and buildings without living spaces directly on the boundary, up to 9 m per side, 15 m in total (average boundary wall height 3 m). The shed would be completely fine there.

There are building envelopes only where there are development plans, right?

That is not the case everywhere. At least in Brandenburg, you are allowed to build garages and buildings without living spaces directly on the boundary, up to 9 m per side, 15 m

Yes exactly. That’s why I also write „mostly“. Everyone has to check their state building regulations or development plan themselves to see where this is regulated – the former is compulsory reading for a builder. A forum cannot describe every federal state here.

If one knew the federal state, one could respond specifically instead of speculating.

Lower Saxony - if I'm not mistaken :)

Such a huge shed at the border is not allowed with us.

You also do not comment on whether there is another building on the border.

Which federal state? Which development plan?

Which federal state?

Still Lower Saxony... ;)