If you’re moving from a GTX 1070 to a 9060 XT 16 GB, I’d focus on the GPU upgrade alone—that’s where you’ll see the biggest performance jump.
If you want to go a step further (and yes, it’s overkill for your current CPU), the 9070 XT is worth considering. You wouldn’t be able to fully use everything the card can do right now, but it wouldn’t hurt performance at all, and it would seriously future-proof you into your next build. It also easily handles a dual-monitor setup.
That said, a 9060 XT 16 GB can absolutely run two monitors without issue. The ideal setup would be one monitor at 1440p for gaming and the second at 1080p for Discord, browsing, or video. That keeps performance optimized while still giving you plenty of screen space.
You could sell both the GTX 1070 and the RX 580 on Jawa—I’ve sold a 6800 XT there and it was painless. Realistically, you’re probably looking at around $150 total for both cards, and that money can go straight toward the new GPU.
Price-wise, the 9070 XT is currently in the $600–$650 range (there’s one shown here at $650). I’m not trying to push you toward the 9070 XT—this is just food for thought. The 9060 XT will already run your games and a dual-monitor setup just fine; the 9070 XT simply gives you more headroom and longevity.
If your plan is to eventually move to the AM5 platform, I’d strongly recommend at least taking a hard look at the 9070 XT. Personally, I wouldn’t put any more money into AM4 beyond a GPU upgrade at this point—it’s an older platform. The smarter approach is to choose the GPU now, then plan for an AM5 motherboard, CPU, and RAM when it makes financial sense. Both the GPU and your current PSU will carry over cleanly into that next build.
One last thing—and again, not pressure—if you’re going to do this upgrade, it’s probably better to do it sooner rather than later. GPU prices have already started creeping up due to memory pricing, and just last month 9070 XTs were closer to $599. That same pressure has started affecting 9060 XT pricing as well.
As for the power supply, you’re already covered. It’s plenty capable and essentially future-proof. No reason to replace it unless it’s close to 10 years old.
I have a correction from an earlier statement: if you were to jump to a 5800X CPU I would get a 240 AIO instead