You don't have anything plugged into the aux jack right? I found when I have my headphone cable plugged in and nothing connected to it I get a high pitched whine (aka ground loop). Not sure if that's what I'm hearing it does sound similar tho.

No nothing is plugged into the aux jack. It's definitely coming from under the hood.

Might be worthwhile to take a run at Nissan seeing that your warranty just ran out a month ago. There's a chance they might work with you. Never know until you ask.

Did you ever get this figured out?

Nope. No one can figure out what it is. Mechanic said it could be a bearing somewhere but there is no way to find out until it gets worst.

Yep, it sounds like a bearing going out in the pump. $1500 though??? way steep. Check with other shops.

Had this exact noise on my G. Started about 4-5 months into ownership. Thought it trans related. Sounded alot like a supercharger whine. Tried synthetic MT fluid which quieted it slightly (in my head apparently..keep reading). Whine was also present when turning the wheel while idling after driving the car a bit. Very similar to that morning sickness like noise that used to be common on fwd cars.

Eventually came across ITB12-035. This replaces the PS reservoir with an updated part. Had this performed recently. No more power steering noise at all, and no other whine which was identical to that shown in the videos in the OP.

The part is about $175 if out of warranty. Replacement should be fairly easy. Was in/out of the dealership in about an hr, test drive included. Good luck.