Been to PC Bhurban from Islamabad airport last year on 1.3 Gli yaris.
There were 3 adults (Including Driver) and 2 Full size loaded luggage bags in the car. The drive did not feel sluggish at all. I think its due to the fact that roads were clear with minimal traffic and the driver know when and where the bends and turns will come and hence know how much power to put pump from the engine before the bend.
also went to Daman-e-koh and monal with 3 adults and one full size luggage bad and still no issue in climbing.
In the end its the driver skill ! I have seen 1.3 manual old school nissan sunny (with 4 adults on board and no luggage) also stall on slopes simply because it lost momentum midway.
however yaris 1.3 engine is different in drive and feel compared to previous 1.3 Corolla engine. i have driven both and the 1.3 corolla Gli engine is more responsive where as 1.3 yaris seems to take longer to respond. just my experience.