The original 2009 boots were not a soft leather. They were/are actually very stiff. The boots for 2013's Into Darkness were copies of those boots, but in suede, which is probably what you're referring to.
Source: I still own an original unmodified black pair.
It seems, to me, like real vintage spectator shoes for women. You can find a similar model for women's dancing shoes...albeit in leather and not with the grey fabric.
It seems, to me, like real vintage spectator shoes for women. You can find a similar model for women's dancing shoes...albeit in leather and not with the grey fabric. View attachment 1837412
The heel shape is very different as the heels for women's shoes only started to be this far out during the 50s, prior to that the heels always seemed to be slightly inwards. That and the cutout to the sides of the shoes making it incredibly difficult to even find a similar style in shoes.