I have a 2015 Silverado 1500 5.3L
LTZ II with dual climate controls.
A/C went out in 2017, and dealer replaced condenser coil (under warranty), worked fine until May 2019. Replaced compressor and condenser. Worked great for 30 days, then one of the line connections at compressor leaked out refrigerant. Replaced the compressor and the line because the threads on both were suspect. Worked great for about a week then began to take longer and longer to cool off after starting. Which progressed to will not cool off ever, unless you rev up the rpms (Won't work if parked, must be driving). After gunning down the hwy for about a mile, it starts cooling fine, and you can drive normally, can even park and idle for extended time, sometimes will continue working after a very short shut off and restart. Was told thar the expansion valve was probably clogged. Replaced it and seems to be even worse now.
I am at a loss.

I would try a different repair center.

I agree, seems like this service facility isn't very experienced in A/C systems.

Yup, it looks like somebody is swapping parts for you, but not actually diagnosing anything . . . and likely doing repairs improperly.

Is this work you're doing. Pay attention to your fan since it'* only cooling while driving and also your pressure switch. Those are the only 2 things it could be if parts were replaced correctly and the fill up procedure was done right.