If you suspect its the battery, best thing to do would be to give it a load test.
I've seen batteries happily charging away at 13 volts and holding 12+ when disconnected, then give them a load test and they immediately drop to 8 or less.
Only taking a superficial surface charge. Bad cell, or the cells are sulfated...
Just a thing that happens to batteries sometimes.
https://www.amazon.com/OTC-3180-Batt...6918388&sr=8-4