HKT (P)-DOH-AUH (A) & return. QR Gold/Sapphire. Utterly confused as to Lounge access in DOH in both directions

If you have QR Gold/ OW Sapphire then you can use the Gold lounge at the A gates and the Platinum/Gold lounge at the C gates
Based on the long haul being "P" I suspect you do not have access to Al Mourjan