Yeah a quick re-write, looking at that parts diagram:
When I said drop it from the transaxle I was referring to number 33 pulley, that may need to come off to get a closer look, apparently it is held in place by TWO number 57 hex set screws, loosen those two then the pulley should CAREFULLY slide off!
You may wish to do this on a solid surface (not on a gravel driveway) because small parts could fall, if a gravel driveway is all you have perhaps put a big piece of plywood or cardboard underneath.
As it's sliding off you want to look for the number 37 key.
If that is sheared or missing, the pulley will spin without turning the center shaft of the transmission (and it would likely make a clicking noise as it does).
I do find it odd however that the pulley doesn't just fall off...
Then again it might be it bottomed out in that groove, as was mentioned the engine pulleys may need to be checked as well... Or there may be a C-clip holding it on to the shaft?
Hopefully that gets you going some kind of way.