It seems to have started already in the late Ediacaran (even before mineral shells) that some things began to go into the sediment (doi.org/10.1130/G328...doi.org/10.3389/fmar...).

Frontiers | Digging Deeper: Bioturbation increases the preserved sulfur isotope fractionation

Bioturbation enhances mixing between the seafloor and overlying ocean due to changes the redox state of the sediment and influences the biogeochemical cyclin...

Just for the record, the shift was probably much more important for the evolution of the benthic macronutrient cycles (Phosphate, Nitrogen). Those are harder to quantify in paleo, but they have been modeled. www.sciencedirect.com/science/arti...