installed it, set the tension perfectly and still doing it...
Here is a video of the noise. Excuse the 2nd half when I turn my phone, but its just the noise I am replicating while driving.

For those with more automotive experience, does this sound like a belt squeal or a pump groan?

https://youtu.be/5EBBQId1Kbc

I sent you a couple of photos... probably a bit late. Sorry, weather was awful for a while here.

Does not sound like belt slippage to me. Sounds like something metal on metal, my experience with pumps 'groaning' are when they are low on hydraulic oil. Except for the Ford CII pump which is a total POS that groans always, even when full.

Hope you find this noise .I would look at the pully on the aternator .With the belt off if you hear any one of the pullys make a noise as you spin them it wants replacing.. Or other could be like that the belt is out of true to one of the pullys.

I would say steering pump .Only thing to make the noise as you turn the wheel from left to the right .You can do as the first post said ,spray it with wd40 see if noise goes away if it did then its the belt Now this is funny but all belts are not the same .You need to count the groves in the old one and then do the same with the new one.You might have one that as extra groves and no place for it to seat in to on the pullys. Did you have the m/b belt .For these sort of jobs i only use m/b part .Do you have the number of new belt.

So I received a new pump yesterday and unfortunately it still is making the same noise when I let go of the wheel and it heads back to center.

Really getting frustrated now...

What else could be causing this issue?
One plus is that it no longer squeals at full lock now! It only does it on returning to center

One thing that after driving last night that I noticed is that I cannot replicate it on a flat surface, but if I drive over an uneven or slanted road it does it.

Now since it no longer does it at full lock, only while driving it seems impossible to find where the noise is coming from.

Any ideas where to look now?

ps2cho, check that the fan clutch bearing bracket doesn't have excessive play due to ball bearing wear/failure. If it's the culprit you will likely observe tiny metal chips below the fan clutch bearing bracket. Best bet for a replacement is a rebuilt one from your local MB dealer. Need to exchange the old one, or pay a core charge.