Cushing's syndrome is what happens when the body is exposed to far too much cortisol for a long time — either from a tumor that drives cortisol production or, more commonly, from long-term use of steroid medications such as prednisone. It's uncommon and unmistakable in its full form: fat shifts to the abdomen, face, and upper back, muscles weaken, skin thins and bruises easily, and blood sugar and blood pressure rise.
It's the kernel of truth behind the "cortisol makes you fat" story, but it's nothing like everyday stress. For someone on a GLP-1, the practical point is that unexplained rapid central weight gain, easy bruising, or muscle weakness are reasons to talk to a care team, not to buy a supplement. See the guide on cortisol, stress, and weight on a GLP-1.