If the Pico is working fine when powered by an ATX supply rather than the brick, then it's likely to be the brick that is the issue
I did not power the Pico with the ATX supply - i just took the 24 pin connector from the ATX PSU and plugged directly into the motherboard.
I guess i could power the Pico from the ATX by using one of the PCIE 12V plugs that would line up with the 4pin Pico input?
So to me I am fairly confident that unless you have a bad unit, which I have never seen (maybe someone else has), you will want to look at the brick, 6 pin adapter (resets at 50% TDP), or the card--though from your tests the card is sounding OK. Maybe measure it's load while using your ATX psu.
Under full load in furmark with the ATX PSU the GPU power TDP% is 98-100% constantly.
I have tried 2 different 6 pin adapters; 1 from 1 x SATA > 6 PIN and another from 2 x molex > 6 PIN. When i tried the 2 x molex i was using both JST headers on the pico if that makes a difference in terms of distributing the load.
The HDPLEX 160W + Dell PA-19 230W brick is incoming but for the sake of learning and playing around with my Pico 160XT i would like to understand what the root cause is.