Turned, left, the steering wheel would not come back?

Hello, did you bleed the air out of the power steering system after the repair? If not we can explain how to, its very easy, you just need a jack and 2 jack stands. Support the front of the truck with both front tires up in the air enough so you can turn the steering wheel back and forth, left to right, right to left while up in the air, this bleeds all the air out of the rack, pump and hoses.

We have a guide to replacing the pump here as well, what was the original issue with the old pump? Just leaking?
I have always had both tires up on jack stands at equal heights so I can turn the steering wheel fully left and fully right a bunch of times to bleed to air out and have never had an issue afterwards, even its replacing and entire rack or just a pump.

https://www.2carpros.com/articles/how-to-replace-a-power-steering-pump

Where did the pump come from? And did you notice any metal particles in the old fluid?
And I see quite a few different 6.0liter vehicles in service info, from the SS model to C1500-3500, K1500-3500. The SS All Wheel Drive is the only one listed with a different vin # at the 8th digit. The rest are all "U" for the 8th digit

This is the procedure listed in service info for bleeding the power steering system. It sounds like the system may still be low on fluid if you read through this.

There is also a procedure listed for (w/ Hydro-Boost) here.

Hopefully no metal particles got into the gear box or rack, which ever it has, There is a high pressure line that goes from the pump to the hydro boost unit, I think you would feel braking issues relatively quick if there was a problem with hydro boost, the brake pedal would be very hard as it would with any loss of braking assist. The ports for power steering are very small though, and hearing metal noises is not a good sign.
Considering you had pieces of the old pump coming out you might want to drain the new fluid into a clean container and see if any more particles come out, I think thats where I would start.
If it has a power steering cooler, those are usually a pretty low point where you could check and drain the fluid as well.
Ive never had an air issue with power steering that caused any type of clunking or grinding noises. I think only a bit of the pump wining while I was turning the wheel back and forth during the bleeding process. Most power steering pumps are replaced due to leaking issues as well. Even running a magnet through the new fluid once its drained will catch any metal just to see how bad it really is.

https://www.2carpros.com/articles/power-steering-fluid-flush

Was there any improvement at all the 2nd time? Do you have the front end jacked up where you can turn the wheel back and forth, and is there any issue with the left turn off the ground?

Is it binding in both directions now?

Does the truck have a gear box or rack and pinion? It sounds like there's still an issue with air trapped in the system. When you have the front jacked up on two jack stands are you bleeding it by turning fully to the left and right as far as the wheel will turn? It usually takes quite a few times doing it, especially since there is a high-pressure line to the hydro boost as well.
It's possible something is clogged up in one of the ports on the gear box or rack, some debris from the old pump blocking fluid from getting into the right turning port, and there's constant pressure to the left turning port. I don't think it's the pump either, when you turn the wheel one direction or the other, fluid is directed to one side of the rack's piston or the other to give assist in that direction. These ports are very small, so something might have migrated into one and that's causing this issue. And another factor is that these power steering pumps are much higher-pressure pumps than a regular system because of the added brake assist.

If the wheel is turning by itself to the left when not moving, then power steering fluid must be being directed to the left side assist, thats the only way the wheel would turn itself like that. Does the truck have a rack and pinion or a gear box with a pitman arm for a steering setup?