I saw this article and was going to post it but it is misleading.
The State Apartments were never the home of Wales.
Apartment 8 & 9 were joined to create the Wales home.
Starting around 2005 apartment 8 was used by The Princes' Trust.
In 2015, William & Harry were interviewed in a room in apartment 8 for the Ant & Dec documentary. I believe it might have been one of the sitting rooms in the 'apartment'.
The writer is confusing, is she trying to state the formal rooms in apartment 8 & 9 were going to be used by William & Harry or that the State Apartments were going to be used by W&H?
Here is a aerial map with descriptions.
http://i.dailymail.co.uk/i/pix/2011/06/14/article-2003249-0C8C757000000578-320_964x821.jpg
Kensington Palace has approximately 80 apartments.
Members of the BRF live in entire sections of the Palace.
William & Kate's current home is 4 stories. It stretches from the clock tower to the State Apartments. It is listed as Apartment 1A.
The Duke & Duchess of Gloucester live in Apartment 1. Only a portion of it is visible on the map.
Apartments 8 & 9 are 3 stories.
Apartment 10 is also 3 stories.
The majority of the other apartments are probably only on a single floor or there are several apartments on each floor. One of these apartments is probably where the office of William and Harry or Diana's post separation office was located.