Gigabyte A320M S2H

Given that it's a budget A320 with very weak power delivery and no VRM heatsinks, it simply seems incapable of handling the power demands of this combo. After hitting triple digits in stress tests, I suspect the power phases are either damaged or just too poor to provide clean power during the transient spikes of the 9060 XT.

Is it possible the A320's VRM phases simply can't handle the transient spikes of the 9060 XT, regardless of the temperature?

Given that the PSU upgrade didn't solve the issue and this motherboard lacks any VRM heatsinks, is it likely that the A320M chipset/VRM layout simply can't handle the power demands of a 5600 and a 9060 XT?

That mobo has no heatsink on VRM at all, before upgrading, you can try to attach some little VRM/RPi heatsinks to them and give it a try, they should run cooler.

It's possible that a low-wattage power supply damaged the motherboard's VRMs.

It's a very poor board, if this issue has followed you through multiple GPUs and a new PSU, I would definitely start to suspect the mobo.