Very fun concept! I'm glad you mentioned doing a post-jam, expanded version because I'd love to play a full adventure game where you could fold into different shapes/vehicles to solve puzzles and reach secret areas and collectables/upgrades.
You could even structure it like a metroidvania where you find new origami patterns around the world and can use those to reach higher/further areas, open previously blocked paths, and maybe even get better versions of previous patterns (e.g. Paper Airplane V2 that lets you fly further and faster).