Same scenario as some: When the IRS didn't take my money by the 15th, I also panicked and went to IRS.GOV and submitted a payment. This means I paid my remaining taxes twice.
Spoke to a nice lady at the IRS, she said that assuming I designated the money correctly (e.g., pay 2020 taxes) which I did (as opposed to estimated taxes), they will catch the overpayment while processing my return and automatically issue a refund. Eventually. She did say that it usually takes several weeks or a couple of months for the refund. She also noted that I can call back after a while and they'll verify that they caught the overpayment.
No need for 1040X or any other form in this particular case, it's automatic.
