Did you try to turn on the switch after wires soldered to all point, basically before wires connected to pico?
This to analyze whether the culprit is on soldering, adapter or it needs to be combined with pico connected that result in this bsod.
When last time you turn off the switch and the first you turn it on again?
Example for me (also its good practice to follow) :
1. Turn off, diassemble all until soc and cleaned all thermal paste on it.
2. Turn on .. ok .. checked. Turn Off.
3.0 For oled you can install Dat0 adapter .. TurnOn .. checked .. Turn Off.
3.1 Install CPU mosfet .. Turn on .. checked .. Turn Off.
4. Install all wires to mobo (3.3v, Grnd, rst, cmd, clk, dat0) ... Turn On .. checked .. turn off.
5. Install wires to Pico ... Turn On .. wait 20 second .. No Sd greets ..Horayyyy...
.. Turn Off.
6. Assemble Heatsink, .. until Metal Shield .. Push/wiggle gently around pico ... Turn On .. NoSdScreen .. Turn Off..
7. Finally .. close the backdoor .. clean the body ..knock on the back door a few times ... Turn On .. still Nosdscreen.. turn off.
8. Done.
And because i already used to it, then now I oftenly if any got problems only on point 6..