Can the apartment ventilation system of controlled residential ventilation enter the sheds?

Most of the time, the apartment ventilation system of the controlled residential ventilation is seen in the utility room, basement, or attic. I have not planned K+S; the space in the utility room is tight. But I have a shed right next to the planned house (wall to wall). Is there any reason against mounting the ventilation system outside the house? A positive side effect would be that the device would certainly not be heard. From when do the lengths of the ventilation ducts become a problem?

If your shed is heated, then that is not a problem.
You only need to pay attention to the penetration into the building.
If your shed, which I assume, is not heated, then that won't work. The devices are designed to operate at room temperature. The same applies to the pipes. You would have to insulate them at great expense.
The device itself, of course, too. And by this point at the latest, your admittedly good idea becomes uneconomical. The device would have to be put into a kind of enclosure so that it is still accessible. You normally cannot do that yourself.

Thank you very much for the quick and comprehensible answer. So the device will be placed in the apartment.

If your shed has at least 10 degrees, it is not a problem for the controlled residential ventilation itself. The only thing you need to manage with Armaflex are the cold bridges on the pipes (into the thermal envelope of the house and possibly also the supply and exhaust air). By the way, there are also controlled residential ventilation systems that are installed on the ceiling (about 30 cm device + about 5 cm hanger), so if you don't have much space on the walls, that might be a solution for you.

has outsourced his technical room to a separate little building if I remember correctly.

has outsourced his technical room to a separate little building if I remember correctly.

correct. However, this room is very well insulated except for the door, even though it is not part of the thermal envelope. Although not heated, all the technology is housed there, so it never gets completely cold...