It seems that it could be the GPU, PSU or motherboard (least likely because it's new). The GPU is old and it's the prime suspect. The PSU can still be faulty despite the fact that it's new. Unfortunately in your case this issue seems to be rare and troubleshooting will take a lot of time.
1) Remove the cable extensions. Maybe the PSU and/or GPU don't like them. A single cable overload could trigger a protection mechanism inside the PSU shutting the system down. So try to operate your system without those cables for a week or so. If you still get a shutdown, then the cables aren't responsible.
2) Try to use your older PSU or another one (perhaps borrow one from a friend) for some time. If the issue is gone, then the new PSU may be responsible. I once had a customer with a similar issue, but in his case he was getting a black screen after he got a new PSU. In the end the new PSU proved to be fine and the GPU was faulty and slowly dying. It was a 4+ year old model it had only worked with the same PSU all it's life. But the old PSU was providing the GPU will lower +12V voltage. When the new PSU was providing the right voltage the GPU couldn't work anymore and all its failing issues came to life.
3)Testing the GPU is more difficult. You have to either test it in another system for a good amount of time or test your system with another graphics card that has similar power draw and preferably an Nvidia card since getting an AMD GPU and changing the drivers could cause more issues.
You have to make sure that all those tests are done for the right amount of time in order to come to the right conclusion. For example, if right now you are getting a shutdown every 2-3 days you have to test your system for at least 5 days and you have to game a lot (lol). Good luck.
EDIT: I forgot to mention that you could stress test your system (CPU and GPU). It may help you pinpoint the suspect. For more info on stress testing read this =>
https://www.tomshardware.com/reviews/stress-test-cpu-pc-guide,5461.html , and this =>
https://www.tomshardware.com/reviews/how-to-stress-test-graphics-cards,5449.html . In your case the GPU stress testing should be the most important thing to look into, as a failing GPU will have trouble completing those stress tests. However keep in mind that the GPU may fail those tests but the cables or the PSU may still be responsible for this issue so test them first with steps 1 & 2.