Will their errors & omissions (E&O)insurance cover this?
There is often E&O insurance but it won’t come into play without a lot of litigation and possibly a proof of insurable loss. In this case the design team has maintained they made no error. The used deep foundations with side friction bearing and designed for some differential settlement.
All buildings not on deep thickness bed rock settle due to the “dead load” of the structure. Subsidence is acceptable if it is designed for and happens in a uniform manner. The designers are maintaining that initially all was within limits and later a de-watering effort of the nearby construction disturbed their building’s bearing due to the water coming out of the deeper material causing it to subside. This is a real concern and it causes some urban designs to incorporate a deep concrete slurry cut-off wall around the perimeter, of the second building — another hellish cost item.
In the case of the Hancock Tower, this is why for the last forty years drilled deep caisson foundations have generally been supervised/monitored during installation in a continuous process as the contractor has drilled them. As waste material comes up, as the bottom and sides are inspected prior to concrete placement the observing engineer confirms what the designer planned on encountering. Deep foundations have often placed a “test pile” or test unit where load is imposed and subsidence measured. If the subsidence curve isn’t hyperbolic showing decreasing subsidence the design must be altered to account for it.
There have often been storage silo’s in river bottom areas that when loaded with material they were built to store, subside in an uneven manner and have to be abandoned and removed.