I suspect you are using reman parts. For the PS pumps either get NEW or pull one from a wreck in a junkyard. The junkyard one was likely working at impact. Reman is something that was ruined and maybe repaired properly or not. If not the debris from a possible pump burn up will dust the entire system. Last reman pump I will ever use was a snow globe in the oil and the shaft quit touching the seal. So in 30 min it had dusted the system and started leaking from grinding new clearances. I had to replace the HB, PS pump, steering box, hoses, flush the cooler, and added a in line filter.
Off the cuff fluid flow goes from pump to the HB unit: then to the steering gearbox. This means the brakes get dibs on pressure and can take it all leaving nothing for steering.
IF the brakes worked you could look at the steering box, but, they don't. Pump or HB...
So something like a kinked return hose off the hydro booster keeping the brakes applied is possible. So is a leaking accumulator in the HB. Are the brakes soft or firm to apply before engine start after sitting overnight?
If the accumulator is leaking down it's going to want to be charged up as soon as the engine starts. A weak pump may not be able to generate enough pressure and they sit fighting each other. Pump can't get any flow and accumulator has the flow blocked waiting on pressure.
The internal pressure relief valve on the pump may be wrong: for a gasser with PS only and set too low. Rebuild outfits don't take the time to care about special diesel settings in the PS pump for the HB. So the pump may be bypassing through a weak gasser relief valve until the HB accumulator can charge up and release the pressure to the rest of the system.
What oil you running in the system? Had a GM that had a TSB to use a revised synthetic fluid due to stiff steering.
Some outfits can put a pressure gauge on the pump. IMO start with verifying proper oil then replace the PS relief valve to make sure it's the proper diesel pressure part. If it's a reman pump odds are good it's just a junker with a poor paint job: replace it with better.