Very similar nuts are made for holding the panels on electronics cabinets made by companies like 'Vero'.
There the nut and spring are square in plan, and the spring has two channel-shaped lugs that grip the sides of a square hole in a strip stamped with them, rather like a 'Meccano' component.
The nut can float sideways slightly to align with the screw but is otherwise restrained by the folded spring.
The suppliers sell a special form of pliers for inserting and removing the nuts in the frames without grief. They cannot be simply be tapped into place.
Errr, how do you think I know about the grief of having to improvise, frequently, with pliers and screwdrivers…?