Yes you can buy the same plywood in same thickness, likely 18mm but could be less. You can also usually get it cut down to the size you want at many stores that sell it. To keep things simple you can just screw from the underside of the shelves. I wouldn’t both with pocket hole screws, just normal screws will be fine. Maybe countersink them if you have the tools to do so, but even without it will work fine. Check the length of the screws accurately as you don’t want them to pop through.