Coolant, battery, and brake light turn on at once, ps no work either

[Raptor]

AC belt doesn't go around the water pump. It has it's own belt driven off the crank pulley. The water pump pulley has 2 belts, one drives the PS pump and the other is shared by the altenator and driven off the crank pulley. If you lose the altenator belt, the waterpump is no longer driven and therefore cannot drive the PS pump.
You can cut the AC belt with no issue whatsoever and all you will have is no AC.