The 3/4" plywood ladder frame that carries everything; KALLAX units are infill between the stiles, not structural. All frame members are 15 7/8" deep (15 3/8" carcass depth + 1/4" backer on each face) — this view is a straight-on elevation of the frame, same orientation as the bedroom view (left wall on screen-left).
The whole assembly sits 3/4" clear of each side wall so it passes in front of the baseboard without notching. Above the baseboard, that 3/4" gap takes a cleat screwed into the studs — this is both the light seal and the lag point for the stiles. Below the cleat, the baseboard fills the gap.