Poor layout of a 4.5 sqm ground floor bathroom with shower

Whether ninety by eighty is enough, I can't tell you. The standard is more like ninety by ninety . The best thing is to go to a bathroom showroom or hardware store and stand in the various sized shower enclosures to get a sense of the space. I would rather choose hundred by eighty then. That should still be very comfortable in size. Only the shower head would need to be mounted intelligently.

Could the door still be moved?

I would rather take 100x80. That should still be very comfortable in terms of size. The showerhead would just have to be installed intelligently.

Would you install it on the 80 side or the 100 side?

On the 80 side and a rain shower. We have such a walk-in shower ourselves. 90 x 150. And on the 90 side we have the shower

On the 80 side and a rain shower. We have a walk-in shower like that ourselves. 90 x 150. And on the 90 side we have the shower

But you shouldn't compare a walk-in shower with an enclosed shower now.
With the walk-in shower, I have to make the shower correspondingly long, otherwise the splashes would land outside the shower. So the showerhead is automatically on the short side. In width, you have 90 cm.

I don't know how you shower, but I either stand with my back or with my front to the showerhead.
In my opinion, you need space rather for freedom of movement of the arms. At least I always bumped elbows in our small shower (75x80). So if you stand with your front or back to the showerhead, you rather need space to the side and 90 cm seem sufficient for you. Why it absolutely has to be 100 cm in the small bathroom now is beyond me, especially since it is an "emergency shower". Of course, for the feeling in the shower, the bigger the better, but that comes at the expense of the sense of space in the bathroom. We also have such an "emergency shower" in the guest WC and after a year have not even used it once. However, our child is only 2 and cannot shower alone yet.

I also don't quite understand placing the showerhead on the short side (unlike the walk-in shower) considering my reflections, especially since with the current location of the sanitary fixtures a nice closed recessed installation could be made.
Maybe I'm wrong and one needs more space to the front, e.g. women for shaving legs or similar.

Perhaps one should try to trace the movements in practice while showering.

I don’t know how you shower, but I either stand with my back or my front towards the showerhead. In my opinion, space is needed more for arm freedom. At least back then in our small shower (75x80), I always bumped my elbows. So if you stand with your stomach or back to the showerhead, you need more space to the side, and apparently 90cm is enough for you. I don’t understand why it has to be 100cm in the small bathroom, especially since it is an "emergency shower".

That’s well explained! It seems to me anyway that the space requirement in a shower is generally overestimated. You don’t stand forever and generally not with arms stretched out or bent in the shower. The walled-off space where you move counts, or of course the space that is free. In this case, I would see the window as a hazard. Maybe you can prevent moisture with a small wall?!