Then he gets a 4060, I've got two of those for my small boys they work perfectly for everything they've thrown at them so far.
I've got a 4070ti Super in this rig, and my oldest's. These cards have the memory volume to play with LLMs locally, which is what they're for. They are certainly a MUCH larger investment.
And I'll continue to point out team red's option of a Radeon RX 7600, it's quite comparable to the 4060, but has a lower price point. You do lose out on some features, but if gaming is the only goal it should do fine.
A couple final notes, we are 1 month away from the 5060's launch... waiting may be a good idea too. I still think the primary failure you're fighting is the PSU, he'll need a decent one of those for the new rig as well. Go get a Seasonic 850W, it's $150, and will probably outlive all of us. The issue you're describing sounds like ye olde "lights on but no one home" problem associated with the 3.3v rail going low during post. Those tend to be intermittent, until they aren't. If this assumption is true, a PSU will light up the current cards and free you from risking the new GPU in the old main board. If the PSU gives you fits later, best warranty on the shelf.