The strength comes from the thickness of the foam - at 2" thick you're getting an incredible advantage versus a 3/4" thick wood tank or a ribbed frp tank or just a thin fiberglass tank. Any tank wall has tension on the ouside and compression on the inside - with a thicker wall core, you're basically giving leverage to the fibers under tension. If you leave the inside and outside skins alone and just double the wall thickness, the stiffness goes through the roof. You could get even more strength with careful cloth selection. In the end this approach wouldn't make much practical or financial sense compared to a wood tank, but it would be a super fun engineering project.
With regards to passive cooling - why not just put a ground source loop in under the concrete and circulate the water through a heat exchanger? Then you're taking the concrete out of the picture - after all, ultimately, the cooling effect is coming from the earth under the slab, not from the slab itself. Could just use a coil in the air to cool the room, wouldn't have to be in the water. With that much water and that much surface area, you wouldn't really need to cool the water directly. If you concentrated on keeping the entire room at the right temp, the water would be there naturally.