We have 3cm soapstone with no plywood but we don't have ikea cabinets.

Generally speaking, I understand the same as Debbi - yes for 2 cm, not necessary for 3 cm.

There is no plywood needed.

We have ikea cabinets and 3 cm soapstone and no plywood. I did use the ikea brackets on the sides of the cabinets to bring the sides up to flush with the metal pieces on the front and back of the ikea cabinets, so all sides of the cabinet would be touching and supporting the stone.

There is no need to add plywood on top of the existing base
cabinets. This will raise the entire countertop up the thickness of
the plywood. Which means you will see the plywood edge at the front.

However, since these are Ikea cabinets, the cabinets are supported only on the metal strips or stretchers. Ikea
typically supplies these small metal pcs to apply to the top of the
base cabinet to level off the base cabinets consistent with the metal
strip. We recommend adding strips of wood on top of the base
cabinets to keep everything level to the front metal strips.

Soapstone
is extremely heavy at 22 lbs sq/ft, so we also recommend adding wood cleats
at rear of base cabinets, where you can, to add additional support.Hope that helps.