Expand the house or a crazy idea

Yes, rerouting cables is complex and expensive; the details would have to be discussed with the utility companies and installers. In my opinion, however, your plan is significantly more complex and expensive.

In NRW, a concrete project with an official site plan, which is an essential part of the easement, is required for the easement registration. Easement areas that are not needed at all are usually not registered. Your (and also my) extension, unlike the carport and the garage, triggers setback areas that partly lie on the neighboring property (presumably 55cm). If these are already secured, you’re lucky; in NRW, however, that would not be possible.