The method of construction isn’t up for debate here, the point of constructing it in this way (as I said in the first post) is to use the same construction materials and methods as the main house.
I understand that to be exempt it shouldn’t contain sleeping accommodation - it doesn't, it's overall purpose is office/storage.
We may (or may not!) sleep in it for a bit.
Schedule 2/ class 6 of the BR states
To my eye that means it doesn’t require BR approval.