Home DIY

I used to work for a company that manufactured ventilation equipment. Basically you have to create a flow of air from an input point to the extract point. In a perfectly sealed room you will not generate air flow you will essentially create a mini-vacuum and it will seem like your fan is not working.
Couple of questions - is there a ventilator in the window, it is normally a plastic looking strip that can be opened and closed?
If Yes and your extraction point is above the toilet (as shown in the plan) then you will effectively create a short flow between the window and the extractor. It will do little to extract the steam from the shower or the bath. You should consider moving that extract point over to nearer the shower.
If no, Is there a vent in the bathroom door or does it fit poorly? If so then the flow of air from the door (when closed) to the extract point will be reasonably effective at taking the steam from the shower and the bath + those lovely toilet smells.
If you get a suitable in-line fan for the loft then you could use it with a Y fitting to extract above the toilet and the shower, air will take the path of least resistance to you may need to balance the ducts to achieve this.
From memory, but worth checking, since you are putting the electrical unit in the roof you will not fall under Part P of the building regulations.
This is the company I used to work for (I managed the technical support team for a while but am not a ventilation technician), a call to their tech support line may yield some good advice.
https://www.greenwood.co.uk/intermittent-extract-fans

Hope this helps.