If you're getting 3-4hrs sleep a night, how do you feel when you exercise, do housework etc

I'm constantly running a bit hot, I'm drinking and eating enough, bloodwork comes back fine..

Anytime I exert myself in the slightest I'm burning up & dripping with sweat. Everything from hoovering to a gentle walk sends me sweaty and feeling like it's a humongous effort!

I'm constantly being told I need to exercise more (because that's going to cure my insomnia..) but I'm physically exhausted 5 minutes in (no exaggeration) whether that be treadmill or weights I feel like I've nothing to give.

(I'm on hrt (peri) and this has never gone away, so part of me is concerned this is coming from too little or too much hrt)

Does anyone else feel like this, is just pure lack of sleep?