maybe something like 2 or 3 of these with a board mounted on the side of the bed..

https://www.amazon.com/Linear-Actuator-Stepper-Milling-Machine/dp/B07K7FWDZJ

with a microcontroller and stepper driver you could have it compress and release pressure from the side.. if concealed underneath it I could see it working and it would use the mass of the bed itself to quiet it down..

steppers aren't silent but newer drivers are much better at keeping the sound to a minimum.. I find the sound of steppers doing their thing kinda pleasant.. almost musical.. (look for videos of 3d printers with sound if you want to hear what they sound like)..

I would be a bit concerned about the safety of the system when it decompresses so maybe some type of flexible barrier to keep your hands out of the pinch area as well.. definitely not a simple system but it would be doable