Once Slate is back on the Tree in Chapter 19, we find that the minister's quarters are very large.
Doesn't the Tree have limited space? How could they justify allocating an inordinate amount of interior volume to one man?
The answer is that the minister's quarters weren't originally designed for one man, rather for a Family, with a capital F.
Remember Larstrun? Slate's and his great grams were interconnected. Slate came from the lineage of a Great Family, while Larstrun descended from a slightly less elevated line.
Slate's Family line (and others at his social level) took over the ministry jobs, while Larstrun's kept the bureaucracy functioning.
The minister's quarters were once the ministers' quarters (a difference in the apostrophe), but that was long before, and now, Slate had the massive space to himself.
It was something he quite enjoyed after his many years on the Factory, living in accommodations that were little more than shipping containers with beds inside.