You can safely leave cooked potatoes sitting at room temperature for up to 4 hours and any longer than 4 hours then the cooked potatoes should be thrown out because they can start growing bacteria and could make you sick.
After cooking the potatoes it's best to refrigerate the cooked potatoes within 2 hours of cooking them if you're not eating them within those 2 hours.
If you leave your cooked or baked potatoes out longer than 4 hours then you can increase your chance of getting botulism contamination, especially for foil-wrapped baked potatoes.
Botulism if not treated soon enough can lead to death so it's not worth the risk of getting botulism so if you left the baked potato or other cooked potatoes out longer than 4 hours at room temperature then you should throw them out to keep from getting sick.