See my post from 25 Jan 22 07:10 in part 15 for the full drawing sheet which shows the pile layout, as well as the perimeter retaining wall cross section which gives insight into how the pool deck level slab transferred load through the retaining wall and down into the outermost ring of piles below the basement level slab.
I don't think as a group we know for sure that the pool-deck-level slab was a critical structural element from the standpoint of maintaining stability of the building itself, because no one has done the big heap of math needed to figure that out... but based on the pile layout and the detailing at the joint between the perimeter retaining wall and the slab, it appears that one of the following is true:
1) the pool deck level slab was a critical element for maintaining lateral stability, and its failure put the foundation system into an unstable condition (in other words, sawcut out the pool deck slab and the building is now unstable)
2) the pool deck level slab itself was not critical for maintaining stability of the foundation system, BUT the failure of the pool deck put unaccounted for horizontal load into the foundation system through catenary action as the slab came down, and those horizontal loads caused localized failure(s) at the joint between the exterior pool deck level and the perimeter of the actual building, and those horizontal loads and localized failures put the building into an unstable condition (in other words, if you sawcut out the pool deck slab the building is stable, unless you then put some big horizontal loads into the top of the basement columns)