When I check a system where the battery could be bad or the charging could be bad:
I test the battery volts on the battery posts themselves. This voltage will be the highest is is going to get during the test, unless charging happens. Write that value down.
I start the vehicle, give it some throttle, and I test the battery at the posts themselves, and at the post clamps too.
(If there is no charging, this voltage will be lower than before. You took charge out of the battery during starting. The voltage cannot be higher..unless there is charging.)
If the voltage is higher at the posts after the start, there must be some charging.
If the voltage at the clamps matches the voltage at the posts, the connection there must be clean enough for charging to happen.
If there seems to be no charging, I have to clean all connections from the battery to the charging source. Repeat the test. Still no charging? Charging has gone bad.
Battery: I have desulfating chargers. I charge them. I look for tiny bubbles floating to the top more or less equally cell to cell. No funny smells, and no violent bubbles. I don't have a battery tester, so if I didn't like what I saw while charging, I take it to a place that has a tester, and batteries for sell. My battery is either found to be good, or I arrive home with a good one. I buy the battery with the most cold cranking amps. I don't judge it by weight per se. If the cooling fan of the tractor blows over the battery toward the radiator, I buy sealed batteries. Otherwise, I buy vented maintenance required types.
Good luck!