When you are immediately at the critical angle, and holding it, in level flight, you will then be at max rate and min radius.
It is all very elementary, but can be made as complex as you want, the basic facts however, are always right!!
Except, ithinkso, those
aren't the basic facts!
Rate of turn is, as you say, a function of AOB/V.
But radius of turn, contrary to what you say, is a function of V^2/AOB.
In consequence, as has already been explained by BEagle and myself, the speed for maximum rate of turn is higher than the speed for minimum radius. And it's not possible to have a sensible discussion on this topic without considering limit load factors and also power available. Which makes it not quite so elementary.