Galaxy S6 won't charge after drain to 0-1%, cannot boot
I got the chance to attempt to charge the phone via a wireless Qi-charger which, to my surprise, worked. So it didn't seem to simply be a dead battery, or a weird software loop, but something specifically concerning the USB/charging port.

I decided to bite the bullet and had the phone repaired. They replaced the "Charging Port Flex Cable", a part that can be bought online for 14$ or less, in case you feel like replacing the part yourself.