PC randomly freezes, no crash dump

Context:

I recently upgraded my GPU from a rtx 1060 to a 4060. The freezes started after that. They only ever happened when I was playing a game. It happened with 3 different games so far, so I've discarded the possibility of a particular game update causing it.

Freeze description:

When the freeze occurs, the PC will no longer respond. The becomes locked in an endless stutter that somewhat resembles static. Pressing the reset button directly doesn't reboot the PC — but the audio stutter stops, somehow. The image on the monitor, which is constantly frozen, keeps being shown on the screen even after pressing the reset. If it matters, the monitor is connected directly to the GPU via an HDMI cable.

Nothing works at a software level after it freezes (mouse doesn't move, etc.), and I can only turn it off by holding the power button for a few seconds.

What I've tested:

So far I tried monitoring temperatures, but nothing seems to be overheating. I tried stress testing the new GPU using Furmark, but nothing special happened even after a couple of hours of stress testing. As I've mentioned, the crashes only ever happened when playing games that would use the GPU to some extent (Baldur's Gate III, POE2, and MHW: Iceborne, if it matters). I never crashed when playing lighter games or performing non-intensive activities on the PC. Leaving it on for extended periods with no use whatsoever has not resulted in a crash, either.

I used a calculator to simulate how much power I'd need to supply the new GPU. Taking all my parts and peripheries into account, it would seem I need about a 350Wish PSU, but I have a 500W one, so I don't think the problem lies there.

I tried checking the Windows Event Viewer and running WhoCrashed, but found no useful information. Because a it's not a regular crash, it is also not generating any crash dump files, it seems.

What I want to know:

What could be the possible causes? Can it be a faulty GPU? A motherboard issue, maybe? What kinds of other tests can I run that don't involve putting the GPU into another machine entirely? (I don't really have one available RN)

Any help and theorycrafting is appreciated!