Well, I decided to try to fire up the 4x RX 5700 XT rig. And guess what? It powered on, which is better than it did after it "died". Nicehash reports 4 GPUs, which means that 4 are being seen in Windows. When it gets done benchmarking, if it hasn't crashed, I'll run it for a bit.
The driver version that I updated to was 22.11.1, not 22.11.2, the driver mentioned by the video in the OP.
So hopefully I was just plain outright mistaken, and that this rig was just having a bad no-power-on day for some reason (PSU overheated? Shorted? Polyfuse tripped, needing some extended rest?), and it's going to be OK.
As for the rig with the 2x RX 6600 on one 450W Rosewill PSU included with the case, I'm going to order a replacement better PSU (thinking of the BitFenix 600W Bronze with 4 PCI-E 6+2 pin, mentioned in Hot Deals), and see if I can't revive that one.
I'm pretty sure that the PSU just plain up and overheated and died in the rig with the single RX 5700. It was prone to overheating, and I've had two of the same model PSU overheat and died in a friend's rig, sequentially even.