This is significant air stratification and is likely the result of improper duct design, not just because there is a slab.
If you do not remove the unconditioned air from the floor it cannot be treated at the equipment. Hot and cold fluids do not mix well, so blowing warm air into a cold room is not effective.
Air conditioning/heating systems are" suckers" not “blowers” as everyone precives.
The supply and return registers are probably both in the ceiling. (?)
This causes the conditioned air to short cycle back into the return register without affecting the air at the floor. This condition can get so bad that the furnace may shut off on high temperature sensors.
This is also an efficiency loss as the extremely high temperature difference at the ceiling and upper walls cause faster heat transfer to the outdoors.
This design will work fine in the air-conditioning mode because the cold air falls to the floor from the supply registers and the hot air is being removed from the ceiling where it rises to.
It should also be noted that you cannot design an air duct system to function efficiently in both the heating and cooling modes.
Adding a second return air register at the floor level and switching which register is being utilized between heating and cooling will correct the situation. If you have to pick one location over the other, supply at the ceiling and return at the floor is your best option.
Have fun with this one! You’ll have nothing but arguments from the HVAC and general contractor.
Wrong is wrong, no matter how often you do it, it still remains wrong.