so, have you had your brakes checked? Many places will check your brakes for free.
The noise was very light listening you your recording. Do you know if it sounds like it's coming from the front or the back? Left or right?
Some brake pads have wear sensors
on the pad that will screech when they touch the rotor.
Some pads screech because they are vibrating as they contact the brake rotor. If they pads are not making noise due to a brake sensor, then it may just be vibration. See if all the factory anti-rattle hardware is present and in good condition.