Hello
I would attach a mechanical oil pressure gage first, for peace of mind and to correlate those readings with the prior electric gage values. I prefer a mechanical gage, with copper not plastic tubing because they are very reliable. I sure hope that the sender is bad. My instinct is that it is.
On the PS pump, I described how we rebuild them on the other forum a few times, and I like it when guys do several things
I like to see guys test their alternator for example,find the bad diodes, or brushes, turn and polish the slip rings, add bearings or whatever it needs, a diode trio, just use the Ford service manual and rebuild it yourself. I try to help guys understand that it is not that hard.
Same deal on a PS pump, get the kit, with o rings, press the bushing, change the shaft if need be. You have vanes to hold, but the factory manual explains it.
Same deal with a starter. Add your own bearings and brushes, a bendix maybe, the felt 'brake' washer, whatever you need.
NAPA is good about stocking your small parts, and you can turn any driver you need, on a lathe, to press a bushing in and out. I see that ROCK AUTO also sells many small parts, which I use at times.
I say this, because many of us had no choice back when, and if you have a good core, especially if original, we try to save them. You usually get a much better result and you learn.
A good rebuilder is also an option, they are out there, as is an old school mechanic who still rebuilds his own pumps,starters and such. Yes, the average store bought rebuilt part can be less than perfect, and often, it is painted everywhere, so it does not look OEM.
Your whine, sounds like air. It often is. I'd have to hear it, it is not the belt, right? Assuming it is the pump/hoses/slave
Check the layout of the high pressure hose, and return hose. That's the one with a metal tube. Often, you fire the car safely, and sometimes have to 'crack' the fitting at the servo, or steering gear. You just follow the high pressure hose,to where it ends,then, as the car runs, back that nut off, just a bit,and cover with a shop rag, and see if bubbles drizzle out. When that ends, and you have clear fluid, the noise can go away
I have seen them just fizz tiny bubbles.
Letting it set over night, can help too. A clue is, look into the resovoir for bubbles. After it runs, pop the cap, and look, or pull out a sample with a turkey baster or whatever you have. Hold it under good light...see any fine misty looking bubbles?
Sometimes, cracking the soft, return hose, at the clamp, can purge some bubbles too. If you just crack a flare nut, or clamp,you create a leak, and the bubbles have a way of migrating out some times. Of course, keep your resevoir topped off.
Also;
Don't lift the car, and turn the wheel lock to lock, that can exacerbate the problem. Don't do it on the ground either. That can aerate the fluid,and it stays that way for an hour or more, so bleeding is harder.
Often, you can bleed the return, as a helper,slowy turns the wheel, a turn or so right, then left, just stay away from full lock.. That can coax more bubbles out too. The front end is jacked up usually, but I have bled on the ground too.
I'd bleed it first, it should be OK if that new.
Sometimes,if the return hose is too long, it can make a high arch, that traps bubbles too. So I have laid the hose over, and lower, to help the bubbles move away. The high point in a line, can be an issue. Sometimes you shorten the hose to flow faster/better too.
If I could see it and feel it, this would be easier, I hope that this helps
If you change the pump, or a hose, you have to bleed the system usually.
But, a worn pump can just be noisy, so if all the above fails, you get another. It gets turned in, they add soft parts, sell it again, and the next guy goes through the headache !
Good luck.