Convert string into char array in Arduino?
So after a lot of help and some tweaking, I finally got it to work!

String text = server.arg(0);

char buf[text.length()];
text.toCharArray(buf, text.length());
char *p = buf;
char *str;
char bitmap[960]; //960 is fixed for now, need to count amount of commas + 1
int i = 0;
while ((str = strtok_r(p, ",", &amp;p)) != NULL) {
  bitmap[i] = strtol(str, NULL, 16);
  i++;
}


bitmap now contains all the XBM data from the GET request. I ran into some issues, causing the device to restart, because I accidentally forgot that the length of the bitmap array isn't 114 (that's the amount of horizontal pixels of the display). This caused it to overflow by a lot.

Huge thanks to jose can u c for helping me.