I am concerned about any of your tests with the power supply in the circuit. A good power supply should have overload protections that might kick in. It could also be interacting with the car’s protection systems.
I don’t think you have clearly told us the symptoms you had when the whole problem started. Charge the battery (when it is completely disconnected), tell us what voltage it has reached, and then tell us what happens when you connect it in the car…ignition off for a couple hours…and measure the voltage then. Then start the car and take measurements. Voltmeters and ammeters, not power supplies.