Whimsical-Industrial. If you look under the red mesh nets it’s a dizzying bottomless darkness- which is precisely why the Doctor will elbow you and tell you not to do that. Steel support column Always looks dazzlingly a bit impossibly spiraly and a bit straight, from every angle it’s a bit off. The corridors are very steel-and-piping but the Inhabited area have a lot of that cream plastic / marble / leather stuff, a bit TNG enterprise. Oh, and the chair is suspended from a rail in the ceiling (well, it’s from the columns, so it doesn’t intersect the pipes), so it can go around the controls- my Doctor is disabled and it’s Helpful to her. Later I discovered this, a similar- even cooler, actually- real life example, and something I feel the doctor would like.
…Don’t worry about the red vein thing. The Tardis does Not like Missy much.