Do what my old boss taught me .... if you dont understand it physically push in the contactor to see what happens.....!!!:nonod:
I asked wouldn't that over-ride any control and more so safety systems...which he said 'we are just proving that the contactor is letting power through and you also can find out what it does as well if there are lots of them' ...
Even at my age I still to this day enjoy the challenge of finding a fault
The start/stop button in the OP is basic stuff and any fault should be easily traced with a couple of 'dead tests' on the control circuit.
No need whatsoever to close the contactor manually onto a possible seized motor..............dirty pants time if you do lol