Without any insulation on the shell, the water is basically in contact with the cold air making its way in and around the tub interior. The shell itself is very thin, even in a rotomolded tub so it has almost no practical R-value. The foam insulation that is supposed to be sprayed on to it is what gives it the heat retention properties.
You’ve certainly done enough analysis to show how poorly it’s performing. The manufacturer ought to make this right and just send you a new tub with the correct insulation installed. Seems to pretty obvious that they screwed up and sent you a tub with no insulation. Or maybe this is how they insulate their tubs and they’re just not designed to be used in such a cold environment. Either way, the manufacturer needs to step up.