I tested the bathroom 1 out by putting the shower on and closing the window. The fan didn't seem to make that much difference to condensation levels.
They don't; they can't.
Is that a comment about bathroom fans in general or specific to the airvent fan that was fitted?
No. Physics.
If you have high (relative) humidity in warm air (shower) and cooler surfaces condensation will occur.
Unless the fan can
instantly remove all the water vapour (which is impossible) then condensation will occur.
Fans cannot remove or change all the air in the room. They draw air out at a single point and it is replaced from a single point, likely under the door. This will cause a weak flow of air from the bottom of the door to the fan with very little mixing.
Surely they must be doing something to reduce condensation levels otherwise what is the point of them?
That is a good question.
Preventing smells travelling to the rest of the house is one 'point of them' - by expelling air from the bathroom and it being replaced by air from the rest of the house - eventually drawing in cooler or cold air from outside.
By doing this,
eventually the condensation will evaporate and disappear. Unless there is a fundamental problem with the room (cold spots, excessive relative humidity in the house with little heating and general ventilation) this will occur within a few minutes anyway without a fan.
It may be that the rest of the house is very humid - sealed kitchen, lots of people and plants, washing drying etc. - drawing this humid air
into the bathroom will cause it to condense on the cooler surfaces.
Leave all the doors and windows open permanently - there will be no condensation.
Therefore, if you think you need a fan, there are more serious problems.
I have said before - I managed flats - depending on the occupiers, the same property can be a mould-ridden hovel or a little palace.