ᐅ Bathroom ventilation with moisture issues: vent pipe, condensation, and limited installation space

Hello,

I recently bought a house and encountered the following situation.
In the upstairs bathroom, there is a fixed, non-opening window. In this bathroom, a ventilation duct with a fan runs vertically through the attic and extends about 4.20 meters (14 feet) above the roof. Unfortunately, I am struggling with moisture, and the sensor keeps the fan running almost continuously.
In the attic, I also have the problem that due to the conversion work, the pipes are in the way (see photo), and I need to reposition the branch for the condensate drainage differently. I only have a floor construction height of about 16 cm (6 inches).
Do you have any other ideas on how to implement this?

Thank you

Is this ventilation effective if the duct runs vertically over 4 meters (13 feet) above the roof?

Can I reduce the duct diameter?

I would then run the duct horizontally or with a slight slope sideways in the attic, so I would only have to overcome a vertical height of about 50cm (20 inches).