"Done uploading" but Uno still running old sketch

What was the last project that you were working on when it started failing?

Have you tried the loopback test? It can exclude the 16U2 serial-to-usb converter being a faulty component.

When you press and release the reset button, what is the behaviour of the L LED before the board starts spamming the serial monitor.

Do you have a second board or programmer? If yes, you can try to burn the bootloader again to the 328P.

The usual way would be to upload blink. Alternatively using ICSP and burning the bootloader.