The plan says nothing about that.
We don’t know that. This again shows that plan fragments are not sufficient for forming an opinion. This applies especially to development plans that became legally binding before the introduction of the Federal Building Code, the Land Use Ordinance, and the Plan Symbols Ordinance.
You could get more well-founded answers and assessments if you showed the complete plan here and a current land registry excerpt. Then one could also see how strictly the building lines of the residential houses in the area of application were adhered to and whether the garages actually have to be within the building window, which your existing garage certainly does not.
Yes, there is only the graphic part of the development plan.
But hopefully a legend and maybe also a reference to the legal basis.
"optically from a recessed garage"
Show the full wording.
but why would it have to be 6m there?
It doesn’t have to be; the minimum distance depends on the building height. But information on your planning is still missing. Does your municipality have its own setback area statute?
… or could the shed be part of the house
Yes.
whether I am allowed to come within 3m of the boundary behind the garage
Yes, if it’s not too high.
It has to be within the building window.
Says who?