I know it may seem obvious, but did you check the pins of the BOOT0 switch itself and the nearby capacitor? A stray bit of solder there could cause the switch to appear always held down by shorting either the cap or the switch. It doesn’t appear that the boot0 line goes anywhere other than there and the main microcontroller so the issue is likely there.

It’s worth noting that the job of auto-mounting a removable drive is often hidden behind the popular file managers, if you want to do it without one you are probably looking for the “udiskie” application that does this in a more agonistic/generic sense. https://github.com/coldfix/udiskie. With that running in the background to automount, then you can just access the drives from their auto mountpoints in the default location of /run/media/username/drive_label