I was the "other person" confused by the original title, so hopefully an explanation of my thoughts helps out.
I'll start with the word "sunken". On dictionary.com (which I mainly use because it has an easy-to-remember name and is free) it's exclusively an adjective in modern use and definition 3 is the one I think is most relevant:
situated or lying on a lower level
Using this definition, a "sunken building" being one in which the bottom floor is below ground is entirely valid, regardless of how the building got there.
Using "sunk" as an adjective in the same way is grammatical, but according to the same dictionary the adjective definitions of "sunk" are much more narrow and technical. On the other hand, in my experience native speakers of English would use "sunk" as an adjective interchangeably with "sunken" so either version would be comprehensible.
In contrast, the terms "sink", "sinking", and "sank" only have relevant definitions as verbs. Those definitions exclusively have connotations of something which starts high, and then goes down, which is why I don't think they are appropriate for a structure being built underground from the start.
TL;DR Both adjective forms "sunk" and "sunken" are appropriate to describe a building which is substantially underground. The verb forms "sink", "sinking", and "sank" are not appropriate in standard English for describing a building process where a structure is constructed inside a hole.
(As an aside, in the world you're constructing using the forms of "sink" as slang or jargon for the "build something mostly underground" process you end up with sounds like a fun idea, it just doesn't align with current usage of those terms in the real world)