I’m trying to find out why my power steering went out hours before the serpentine belt even snapped if there’s a logical reason

So at first we were just driving and the power steering went out so we thought it was no big deal went and got more power steering fluid, seemed to help a little, drove about a hour and a half steering was getting rough again put more fluid in because it seemed it had went down just a bit either that or they didn’t fill it to the max line so we filled it up a bit more get about a 15 minutes from where we need to be (3hr drive total without any problems besides power steering) then all the sudden everything else went to shit because at that point is when I assumed the belt came off because yea overheating and all that, so my main question was why did the power steering go out 3 hours before everything else did if there’s a logical answer to that.

Well I mean I was on the a 70 mph rd with my friend her 2 kids in the car Wich one of them can’t walk in the woods with no where to pull off I mean I was totally gonna just sit in the road and risk my battery dying and not having hazards or heat, the turn to my destination was basically the only safe spot I could turn off at, I was just trying to keep people safe and get there honestly man if I was alone it’s wtv but I wasn’t gonna put them in danger

Would you possibly have any answer for me on why my power steering went out way before everything else