... that allows the steps to collapse and the support brace to pivot inwards so that the unit can lay flat? Some sort of bolt?
1 Answer
Dowels.
This could be done multiple ways but I'd say there's a good chance the tread and the riser pivot on dowels. This is the simplest way to make anything like this where a component needs to rotate about an axis, although you could use steel pins* for increased strength and durability a wood-only solution can be strong enough and durable enough for a long service life. The key thing then would be the diameter and strength of the wood used for the dowel.
*Housed directly in wood or in bushings of plastic or metal