From dated memory, the steep approach criteria evolved in two areas; an approach to an airport, without landing from a steep approach procedure vs approaching a runway to land, maintaining the approach angle.
Examples were Lugano, where the approach was into a valley, aiming short of the runway which required the aircraft to transition to a lower - PAPI defined final approach to land (GA terrain issue).
These operations may not require special aircraft or crew approval, depending on the type of operation and regulator (country). Obviously the aircraft had to be capable of flying the initial approach 'path', but not necessarily landing from a steep 'angle'.
Alternatively London City involves landing directly from the steep approach and requires full approval, particularly that the aircraft could maintain the required glide path (ILS or PAPI) in all conditions and be flared from the steeper angle.
Thus if a circle-to-land procedure involves a landing flare directly from a steep final approach, then both crew and aircraft should be approved, but check type of operation and regulation, e.g. USA part 23 not required, part 25 would be; EASA, probably all commercial operations.
There could be wriggle-room for a visual only final approach and need to meet icing configuration / thrust requirements or not, but the flare could still be limiting.
World example - Aspen used to allow approach to circle, but then Nav aids change / improve.