My best guess is, people do sweat, it’s just that there’s no way to notice or detect it since it’s water in water. It would be pretty hard for the body to specifically only sweat from your exposed upper half of body while not sweating from the submerged half of your body.
Furthermore, there is no reason the body wouldn’t sweat there. It’s hot, it’s being exposed to heat, there’s every logical reason for the skin to emit sweat even while underwater - it would feel the need to cool down, even if it were surrounded by liquid.
Google “dehydration while swimming”, and you’ll find many articles discussing sweating while swimming, and how easy it is to not notice how much water you’re losing.
If that happens in a pool, a relatively warmer hot tub will certainly have you sweating.
Yeah, if you’ve ever been engaged in any kind of competitive or long-distance swimming, it’s very clear that you do sweat and get dehydrated, even though you’re in water. You just can’t tell that you’re sweating.