New brakes squeak AFTER I remove my foot from the brake pedal!

Just a wild guess, but perhaps the pads, when not in braking mode, are not parallel to the rotor and one of the tabs on the anti-noise shims is rubbing. When the brakes are applied, they become parallel when grabbing the rotor, and the rubbing shim tab is drawn back when the pad rotates to become parallel. OTOH, if the brake job is new, neither the shim tabs nor the “fix-me-now” squeaker should be anywhere near the rotor, so I don’t know.

If the squeak is rhythmic and not constant, then you probably have some very minor run-out on the rotor, not enough to worry about.