5600 to 5600x3d?

I recently upgraded my GPU to a RX 9070 from RX 6700 and I have a Ryzen 5 5600 with 32 GB DDR4. I primarily play at 1440p on an ultrawide. So far, been loving the upgrade, it's double the performance. But I do notice that my CPU is hitting 100% in some heavy environments when I turn on FSR, makes sense as I'm reducing render resolution.

5800x3d is $300-350, not even thinking about it because I thought I could run this platform for a couple of years and upgrade to AM5. But I saw 5600x3d at local microcenter for $169, and I'm not hopeful about AM4 getting more CPUs at reasonable prices in the future. So I'm tempted to swap but I don't know if it makes sense from a future upgradability perspective. Even if I get it, and a couple of years later if I want more performance, I'd have upgrade the platform. Does that justify the price? I can maybe sell 5600 for 80-90 bucks (hopefully) to cover some costs. Am I overthinking? Should I just go and game on my new 9070 or am I gonna miss out