Does the noise change when the front tires are off of the ground, and the steering wheel is turned (during the 30 seconds in question)?
When did you buy the car? How many miles, when you bought it?
Have you had the timing belt replaced, since its 105,000 mile recommendation?
Maybe, like mine, the TB was done earlier at 80,000 miles. That would mean that you're closer to the 2nd TB job than you think.
I heard that at 105,000 miles 3 internal TB components need replaced and at 200,000 miles 5 internal parts are replaced, because they are worn and get noisy.
I also heard that a couple of mechanics had noise (that hadn't been there before), after they did the 105k TB and they had to redo the job, to install the extra 2 parts.
Externally, at 105k, just the serpentine belt and at 200k both the serpentine belt and its tensioner get replaced.
What is the fluid level in the power steering reservoir? I'm guessing the noise is coming from the pump itself. Also, look to see if the power steering pump is leaking like it is with the one in the video.