I have a very small ensuite bathroom (approx. 5 ft x 7 ft) and I
renovated it by replacing a tiled 5'x 2.5' shower with a 36" corner
shower. There is a small problem with this renovation that we did not
think of: poor ventilation causing severe condensation on the walls
and wrecking the paint.

This is the reason (I think): Normally, in most bathrooms, there is a
lowered portion of the ceiling that goes over the tub. In my
bathroom, this lowered ceiling was kept in tact and the new shower has
a higher shower door, so I think it doesn't allow the steam to
ventilate the same way. We installed a brand new, fairly strong fan
(which is rated to work for a bathroom 4 times the size of this one)
and checked that it is ventilating properly through the tube in the
attic and to the outside of the house. It is.

I have a couple of questions:

What is this lowered area of the ceiling in the bathroom over the
tub/shower typically for? Can you tear this out? Would removing this
solve my problem?

Should I just install I higher-powered fan to solve the problem? I
can buy a super-duper heavy-duty fan that is used for huge rooms.

This condensation problem is especially prevalent in the winter, when
the bathroom is cold and there is more mist generated from a hot
shower.

Thanks in advance for your help!
Paula