It was built by Integer Essentiae ~40 years before PSitME.
Ax and Emma lived here, with the house gaining more residents throughout Season 1.
Between seasons, it housed Nicole and Lilian Essentiae.
As of so far in season two, it functions as sort of a headquarters for the heroes.
There's exactly one thing worth mentioning about the ground floor of Ax's house: when you open the front door, the toilet flushes, and vice versa. Everything is connected - Axiom.
Other than that, it contains the living room (complete with a home theater setup and a table for tabletop roleplay), the kitchen (filled with various cooking devices, a fridge, and some cabinets), and the half-bath with the front door toilet. Of course, it is also the permanent home of the most important character in all of the Taraverse: Ax's Houseplant.