07 Ford Focus, Weird power steering issue when heavy clutching out of first

What is your question?

First off, Thank you for your time! So I can get in my car, start it up and turn the wheel to the left and right multiple times with no issues. But when I have to clutch heavy (EX: Starting on a steep hill) the power steering motor immediately starts whining and turning the wheel left and right sounds horrid, like its out of fluid. This only happens with heavy clutching out of first. If I start on a level surface and do not have to clutch hard everything is fine. If I let the car sit for about an hour, the problem goes away. I'm not understanding how a transmission clutch and power steering motor are somehow connected. Thank You

What makes this problem better or worse?

Letting it sit for an hour