Floor plan design: Convert the study room into a bathroom

Hello everyone,
We are at the beginning of renovating an end terraced house. We want to set up a new bathroom where there is currently a study (red frame in the floor plan). The current bathroom should remain as a guest bathroom.

Since the space is limited in the new bathroom as well, we are working on the optimal layout but have somehow reached an impasse, which is why I am hoping for new input here.

The door should be shifted to the right. We want a walk-in shower (in the drawing the width does not quite fit, it was quickly put together). We want to forgo a glass wall and instead build a wall with storage options ourselves. The attached beige-colored image already matches our idea quite well.

Do you see a different arrangement of the elements as possible?

Thank you in advance.

The floor below is missing. A newly created bathroom requires: 1. cold water supply; 2. hot water supply or heating of cold water; 3. water drainage (downpipe connection or own downpipe(s)). Point 3 is the most invasive operation and also affects the floors below. If all the water (white cold, white hot, and gray/black) were beamed by Scotty, then (but unfortunately only then) the measure would be only a "furnishing matter".

The pipes are already in place and would need to be "tapped" (red and blue). Currently, the kitchen is located below the room.

The drainpipe runs through the shaft. That is why the rough plan was also to arrange the elements this way.