Which graph is the correct representation of the trailing edge flaps' effect on the critical angle of attack? Does their extension increase (as depicted on the first graph) or decrease (as depicted on the second graph) the critical AoA?
Both right and both wrong, both over simplifications based on unknown airfoils, and so on. Real aerodynamics is complicated and 3 dimensional.
Flaps usually increase the critical angle of attack a few degrees, but they also increase the effective angle of attack for a given pitch. So the net result is that the pitch of the aircraft will be similar at stall with or without trailing edge flaps, but the true AoA will increase.