Fans don't stop condensation they merely pump the steam out.
Never a truer word, I looked at three homes, each one had a shower, one had problem with Mould, other two did not, and only one had a fan rarely used, so I sat back and tried to work out why.
What I realised was the problem was the house with mould had the shower over the bath, two sides were walls, one was a glass panel touching bath side, but the last side it went over the bath and caused a chimney effect.
There was a flow of air into bath up the shower cubical and out of top into the whole room, so whole room full of moisture. The problem was this flow of air.
So if the shower cubical seals at the bottom, then no chimney effect, and moisture is not transferred to whole room in the same way.
A fan directly above the shower cubical direct outside will remove moisture, but put the fan in the wall, and it drags the moisture into the room first, and causes more moisture to enter room not less.
Switching the fan on after one has finished showering will remove moisture, switch it on while showering can drag the moisture into the room. Also shower curtains cause problems, mothers wet room with no shower curtain had no problems with mould, as the moisture was only around area of the shower, it did have an extractor directly above the shower, and under floor heating, however both hardly ever used, a quick mop down after the shower and room soon dried.
But I have never moped down a bath, we leave it wet, in fact make it worse by putting anti slip mats in the shower area which retain the moisture. Because in the wet room we did not want the water being walked around the house by anyone using the loo, we always mopped down after use.
You need to address these fundamental problems.
I wish I knew how, my father-in-law lived in an identical house to my last one, his humidity was around 80% my house around 70% and this house at moment showing 60% and raining cats and dogs at moment.
I have tried to work out why, and cooking with gas is clearly one of the problems, but neither of my homes did we use gas to cook with, this house tumble drier in an unheated room with window always left open, last house tumble drier was in kitchen so it pumped out air heated not only by tumble drier but also central heating, both homes have a flue, old house gas fire with flue brick, this house solid fuel fire with nothing to stop rain going down the chimney so should be worse, but is better.
Looked at the idea of a heat recovery unit, but never got around to fitting one.
So I have no idea why this house in Mid Wales is dryer than the old house in North Wales, the humidity meter shows me it is, but no idea why.
Clearly any extractor fan must cause a draft and draw in replacement air from some where, likely rest of house, unless a heat recovery unit is fitted, so this house at 60% has a flying start over last house at 70%. And only extractor is the chimney and the cooker hood, the latter hardly every used.
With an induction hob with auto boil/simmer option, likely less moisture due to cooking, and also less heat into the kitchen, but most of my cooking is with a microwave, so that hardly helps. I would say most likely reason for less moisture in this house is the size of the house, three floors, five bedrooms, three bathrooms, two kitchens etc. We actually have a back and front kitchen, although back kitchen seldom used.
But I digress, what I am saying is look at your home as a whole, open fires, induction hobs, vents to outside all make a difference. Try to work out why your home is damp, be it driving rain, or un-vented gas appliances.
Next is how to address as a whole. Move away from gas cooking, fit heat recovery units, throw out the kids (only kidding) or mopping down after use. Stop looking at just the bathroom but look at whole home.