From your pictures, your battery appears wet where the dirt and dust are sticking to it. That is typically a sign of either overfilling the battery or the voltage regulator is overcharging and the battery acid bubbles out of the vents. When you checked the 12.5V battery voltage, was that with the engine running? If not, check the voltage with the engine running and battery charging.
I do not think it is related but your braided ground strap connection at the tractor frame looks a bit rusty.
I do not think it is related but your braided ground strap connection at the tractor frame looks a bit rusty.