C2 Clutch: Function and Operation

Hello, due to a warranty claim JUL following a complete overhaul of a T5 automatic transmission, T5 MJ2008, 2.5 TDi (not DSG), the smoked-out C2 clutch was identified.
The cause could have been a slightly low permanent engagement pressure on the clutch, which would then cause it to slip slightly, or a software error in the engine control unit (ECU)?

Mileage: 14 months, 46,000 km, then suddenly, complete engine failure.
Highway breakdown.
Therefore, the question is: for which gear(s) is the C2 clutch responsible? The entire slider mechanism was completely replaced at that time.
Is the C2 clutch engaged in 6th gear? It should be, but what if there's insufficient oil pressure at the C2 clutch? It's operated by the new shift box, after all.
Could a transmission oil cooler with insufficient flow rate be the cause?

The transmission was overhauled by a specialized company focusing on automatic transmissions and comes with a 1-year warranty. It also includes a new turbocharger, starter, alternator, water pump, belts, and wear parts.