It certainly seems like your GPU is causing a crash, but it's just as likely (maybe even moreso) that the PSU is behind that.

You can look into things like Furmark, MATS and MODS, etc to drill down further. Northwest Repair has plenty of examples on his YT channel.

Is this a new issue, or has it always been the case with this hardware combo?

If it were me, I'd just get a new (and good) PSU from somewhere with a good return policy. If that doesn't fix it, return the PSU for a GPU. Other people will link to the calculators, and be sure to get a good model from a good brand. Don't cheap out or ignore the subtle details. A bad PSU will pay you back with all sorts of weird, intermittent stability issues.