It would be interesting to use the same optimizers, and the same visuals (btw. very nice) that show what the optimizer does to start at the maximum (2,0) and determine the minimum. Is that at (-3,0)?

When maximising, as you mentioned, there is a nice ridge that "leads" to the optimum and away from the constraints. However, when minimizing,, no such nice feature exists in the feasible space, and the optimization steps taken might have to hug the constraints, particularly the larger circle. It might be that an optimiser does better when deliberately taking a centering step- interior point algorithms often use such a corrector step or combine with the predictor, resulting in fewer steps.