In Europe, a lot of Third Generation Mazda6's, or at least some, were 2.5 gasoline's... and those came exclusively with automatic transaxles. Now generally the automatics are reliable, but recently a fellow on this board had a failure at a lot less than 150,000 km... and he was quoted about US$6,500 for a factory rebuild 😳. The automatic does not have a lot of slip; the torque converter locks up often, and at low roadspeed. That makes for less generation of heat. When towing a carvan, that lesser heat generation would matter, though more slip actually would be better for performance with a caravan... as more slip emulates, in effect, having more gears in the transmission (keeping engine revs in the more efficient range) and some fluid "cushioning" effect. Having said this: i) the automatic is, in my opinion, more heavy duty that the Skyactiv-MT manual... perhaps better with a caravan; but ii) the design of the automatic transmission transmission fluid cooler makes it hard but not impossible to fit an auxiliary air-to-fluid cooler in front of the radiator... which is often good practise when towing a carvan.
In Australia, the Mazda6 gasoline 2.5 is rated at 1500 kg caravan (braked) with 150 kg tongue weight; 1600 kg for the diesel. For other Forum members... outside North America, cars towing caravans are obliged to stick to a lower speed limit... and as you can see, tongue loads are lowish, sometimes less than 10% of caravan weight.
I have seen a video from the UK where a Mazda3 with 2 litre gasoline engine tows a caravan quite successfully... The Testers liked it. It had a 6mt, and perhaps it was not through the mountains. If you live in the Netherlands (flat) and don't venture far from home maybe it would be ok.