I totally messed up and forgot to add supplemental essay on time

I am an international student and submitted my common app application before the local time deadline(Harvard+Amherst). But when I decided to check my application in the morning (6 hours later, but still before the ET 23:59) I saw that I forgot to add supplemental essays for 2 Universities. There is no chance I could contact them via phone till Jan 4th since I have a long flight today + time differences. I wrote emails to both colleges, and they probably won’t answer soon. I am so stressed right now that I wasted even a small chance of getting there because of my inattentiveness. I saw different questions on the same topic here, but the answers to them are all drastically different.

I think that you have done all you could by emailing the two universities. Did you attach the supplemental essays to these emails? If so, it might serve also to convince them that you had indeed finished the essays in time, and honestly did not submit them accordingly.

Not sure exactly what you mean, but a rule of thumb is that anything that is within your direct power (so the application itself, essays, portfolios, supplements etc) needs to be submitted by the deadline, and anything that you are relying on someone else to do/send (transcript, rec letters) will often have a week or two grace after the deadline.

I already submitted them through common app and just wanted to be sure that my application will still be considered