2003 GT Vert - Rear end noise

Maybe...check for the source in that order: tires, brakes, suspension...

Sounds like the rear axle bearing(s), any seepage from the area? Jack it up and check for excessive movement in the bearing.

Turning at low speeds (sharper turns) really exposes differential issues because the rear wheels are traveling at different speeds due to the turn, making your ford traction-LOK differential work. You should check your brakes and tire first because those are easy fixes - they are most likely not your issue because you would notice those issues no matter if you are turning.

The differential clutches wear out with time. Check out the rebuild kits here: https://www.americanmuscle.com/mustang-lsd-9904.html

While you are at it I would upgrade to a finned differential cover.