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Unfortunately, insulation and sound proofing is not required per code between conditioned spaces in this case.
It is also worthy of note that additional insulation between the floor will do very little to impact the noise tranmission as a majority is carried via vibrations on the framing.
There are applications and techiques that can can be deployed. All of them will require removal of the existing ceiling if you stay with a drywall finish. You can run resilient channel in addition to sound de-coupling isolators.
It is not an easy or cheap bullet fix in this case.
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