The "click" symptom usually indicates a severe voltage drop when the battery is connected to the starter and a high current is drawn. This is normally caused by a bad battery with a high internal resistance but since you have eliminated this, I'd say you have a bad joint in the cable running from the battery to the starter solenoid. Or a bad starter solenoid, but I assume that was changed along with the starter (they are usually sold as a unit).
First thing to check would be the BST (battery safety terminal) - it may have come apart internally. Next check that any joints (X6404 & X7163) in the main positive lead that runs from the BST to the starter solenoid are clean and tight.
https://www.newtis.info/tisv2/a/en/e...-motor/bEud1CV
My guess? Bad BST....