No Z-Axis option & more: Newbie trying to get started with 1st galvo fiber laser

Your board looks like this clone, the chips I can read are equivalent. Labeling a little different. Looks like a clone of the old BJJCZ original board, FWIW.
One thing I see in your photos, two microstep drivers, and an extra board. That extra board is likely a step generator for the extra microstep driver powering the stepper on the Z axis.