This is setup I’m working to
The run off would be 21.5mm waste pipe into the soil stack, rather than out of the eves. Air from the soil stack entering the bathroom is a possibility I suppose and something I had in the back of my mind.
Access to the soffits will be tricky as this is a room in the eves/roof space with a small attic above.
However, I might be over engineering the whole thing. I’ve installed the fan and ducting this afternoon. The total ducting used is just over 1.5m. The duct up to the fan runs horizontally and is under the insulation. The duct length after the fan is 0.5m. Essentially this setup would be to catch any condensation in that forms in that vertical 0.5m! I did just think maybe I should do a belt and braces approach with the condensation trap but maybe just insulating the 0.5m duct after the fan will be enough