Redesign existing bathroom planning in a new apartment

since we live on the ground floor

... but the shafts are not located there just for your pipes and would disrupt the modifications for the other floors, this apparently has not been understood yet. Risers and downpipes do not meander, but run straight.

Well, the chamber next to the bathroom can be drained together via the front upper drywall in the bathroom if used as a toilet, since no floor-level shower is supposed to be installed there... The toilet and washbasin just have to find their place at the top or right side, then it will work! And a washing machine in the chamber can also pump up its wastewater, it does not necessarily need a slope.

Well, the chamber next to the bathroom can indeed be drained via the plan-top drywall in the bathroom when used as a WC,

That does not change the fact that the OP apparently lacks the imagination to realize that the shafts do not only carry the supply and disposal for his apartment, but also for all the neighbors directly above; and that you cannot hang a sign in these shafts saying "Neighbors' pipes please use the other side of the street," but that this conglomerate has to arrange itself there. The shafts are planned – and in such a way as to steal as little leasable or sellable space as possible on all floors. "Assuming I were the only person in the world" is an unsuitable basis for speculation when reality takes place in a multi-apartment building. In multi-story residential construction, it's about battery cages for property developers; there is no room for "it would be nicer if" fantasists. Every project has precisely planned suspension points for special requests to extract more purchasing power with options. But these are all in the premium residential units, and a chamber-change ritual in the economy apartments clearly does not belong to that.

The idea is nice, but it doesn't work. I think the main reasons for this have already been mentioned. If you dislike the layout so much that you want to change everything, another apartment would be an option.

Since the toilet is planned anyway in the wall between the storage room and the bathroom, it really shouldn't be a problem to also install a toilet on the other side here. The slope is identical and we are not leaving the apartment here. Most likely, the thick black line at the top of the plan indicates water/sewage, which would be connected here as planned.

Just ask, or if necessary, have the builder provide the plumber's number and discuss it with him.

I also don't have a storage room! Instead, the kitchen is generously designed. Ironing board etc. then in a cupboard. I would definitely take the guest WC. Washing machine and dryer are in the laundry room despite the ground floor.