Does that mean folding allows you to construct (without trial-and-error) an accurate heptagon, even though you can't with a straight-edge and compass?
Intuitively, that seems wrong, I would expect many of the same limitations to apply.
https://origamiusa.org/thefold/article/diagrams-one-cut-hept...
The one cut is to remove the perimeter of the square that lies outside the heptagon. Without the cut, you could make a crease, and fold the excess behind the heptagon.
Certainly good enough for practical handheld construction purposes, but not geometric-proof-y stuff.
Scimemi, Draw of a regular
heptagon by folding.
Proceedings of the 1st
International Meeting of
Origami Science and
Technology. 1989
Are you familiar with Lill's method of finding real roots of polynomials of any degree ? Simultaneous folds are a realization of the same idea
https://en.m.wikipedia.org/wiki/Lill%27s_method#Finding_root...
But remember one is dealing with idealized / axiomatized folding. The situation is similar with compass and straight edge geometry -- those physical lines and circles marked on paper are approximate but mathematically, in the world of axioms we assume the tools are capable of perfect constructions.
http://origametry.net/papers/heptagon.pdf
It shows both a single sheet and a modular version.