There is a very loud squeaky noise coming from the rear that stops when pressing the brake pedal?

More than likely it is the squealers on the pads telling you they are worn. They are small tabs that are designed to rub the rotor when the pads wear down. When you take your foot off the calipers relax a bit and they shift to keep the pads off the rotors by a paper-thin amount. It's possible that when they are in that position the squealer hits the rotor. Then when you step on the brake the caliper shifts and it lifts off enough that it stops. I would say it is time to inspect them. Usually when you hear them the grinding noise of pad backing plate scrubbing the rotors isn't far behind.

This might help in your inspection:
https://www.2carpros.com/articles/brake-pad-symptoms