Pro Micro board not responding to anything
It turns out I had to use the port ttyACM0 (and not ttyS0) which wasn't found at the time. The port was there the next day and I have no idea why it wasn't there before.
Also, I thought I had to press and hold RST for a couple of seconds to reset the Pro Micro, but I actually have to press it twice in a row.
I've managed to flash the firmware for my keyboard by double-pressing RST.