@DLosc Are you considering building one yourself? It's a good way to convince yourself to upgrade parts bit by bit until it's $3k save money
Personally I'd go with an RX 6600 if a 560 Ti was mostly working for you
It's currently the best value-for-money GPU on the market, it's about $200, and it's ~5× faster than a 560 Ti
Since you seem to be the type to hang on to a PC for a while, I'd recommend considering an AM5 build (AMD's newest CPU socket)
It should be getting new CPUs for the next 5-10 years or so, if it lasts as long as AM4 did, so you'd be able to upgrade at any point if you felt like it
Honestly if you were getting by fine with a 12 year old PC and a 560 Ti you might even want to consider a micro ATX build
(IME unlike people claim building a PC does actually cost more than buying a prebuilt, but only because you spend more on quality cooling, PSU, case, storage, etc.)