You unknowingly described our door to a tee.
Works pretty much as you outlined. Hinged on wall the 2 halves are held together with simple hasp, me I call them window sash hasps,
Recently replaced ours.
Locked it acts as single door, unlatched it is bifold.
Latch is all but identical to what is on our screen doors at home.
Inside simple handle to pull closed when unlatched, acting as bifold, slide hasp to retain. Door will stay closed without using the slide hasp but can easily be opened from outside, or if you bump with elbow. I assume height was to keep small child from being traumatized but the loud yelling from outside as door hinges removed...
I would think mid placed latch of some sort if door used as bifold often, ours swings toward camper exterior door so not an issue when stopped on the road for a few
