Impossible does not mean undrawable. It means undrawable exactly with those two instruments, and the workarounds are old and good.
The best-known approximation is Albrecht Durer's, published in his Underweysung der Messung of 1525. Inscribe an equilateral triangle in a circle; half the length of the triangle's side, stepped around the circumference, is very nearly the side of the inscribed heptagon. The error is a fraction of one per cent, far below anything a mason or an engraver could detect, and Durer presents it as a working method rather than as a theorem. His book gives an approximate nonagon in the same spirit.
Exact constructions become available once the restriction is loosened. Archimedes produced a heptagon by neusis, sliding a marked ruler until two points on it meet two given curves at a specified separation; the construction survives through Arabic transmission and is regarded as one of the finest of antiquity. Neusis is strictly more powerful than compass and straightedge, since it solves cubic equations, and it therefore also trisects the angle and doubles the cube. Paper folding does the same work: the origami axioms permit cubic solutions, and an exact heptagon can be folded. A conic section drawn as a curve, or the quadratrix, will also deliver one.
None of this contradicts the theorem. Each method adds an operation that the classical rules exclude. What the theorem states is precisely how much power those two instruments have, and the heptagon marks the boundary.
Seven sides therefore appear rarely in traditional architecture, where the compass governed the drawing board. The most familiar seven-sided object in ordinary use is a curved one. The British fifty pence coin is an equilateral curve heptagon, a shape of constant width, so it rolls smoothly through slot machinery despite having no circular edge; the seven-sided form was chosen so that it could not be confused by touch with any other coin.