Sota TT Motor Board Mishap

Those capacitors are pretty reliable and long lived if you don’t exceed their voltage rating. Since they are non polarized the fact that there was a reverse voltage applied should not do them any harm. If they do not read shorted you are ok. You should be able to test the capacitance value on any DVM that has a cap range.
THE IC’s could be damaged. You can check for obvious short circuits with an ohm meter and checking between the power supply pins and all other pins for shorts. A lot of times the electrolytic power supply caps will short and load the power supply down to the point where not a lot of reverse voltage gets to the ICs. I have seen them survive this sort of thing but not always.