No, the best gaming PC you can possibly build is around the 12900k and a high end Nvidia GPU. Gives you the most up to date everything and 3080 and up is already beyond the point of diminishing returns (I only have a 3080Ti because I got it at retail MSRP, glad I did, price has only gone up since, and I know I am going to keep it a long while to justify the price tag)
Operating within your budget you can opt for a little more CPU or keep it all in the GPU. Generally for gaming at high resolutions or quality the GPU is very important. If you are targeting pure FPS, then CPU matters more.
Depending on what Ryzen 5 you have, nothing says you can't drop a 5600X or more directly in. X370* B450, B550, X470, X570 should all be able to do it with a BIOS update. *X370 is very recent, not all boards have it available yet, and it is completely optional for the board makers.
Borderlands doesn't tend to have the highest requirements. Nice to play with everything on, but for the most part you can halve the settings and it still looks fine. So downgrading to a more reasonable GPU isn't a bad idea. Keep in mind that you can sell that 2060 Super for several hundred at the moment. Still outperforms the new RTX3050 for example. So you can recoup quite a bit of what you spend on the new system.
i5-12600K 6 cores 12 threads Plus 4 efficiency cores (roughly Skylake/Kabylake in performance)
Single Thread Passmark rating : 3968
Multi Thread: 26914
Ryzen 5 5600X 6 Cores 12 Threads
Single Thread Passmark rating: 3381
Multi Thread: 22138
The idea being that Windows 11 will put low priority tasks onto the slower cores, leaving the full power of the big cores for your applications. It is a huge change in design, but this is only the first generation of it.
Now getting a GPU is a bit of a problem, but there are certainly ways. Without the cost of a full PC, you could just pay the scalped premium for a card for example.
Hard to make an argument for an older Intel with the 12400 and up around. If I were building right now I would probably make the attempt to get a R7 5800X3D when that comes out. Should put Intel back in second place (maybe). Or hold out for AM5 later this year. The big downside to AMD right this second is that AM4 is end of life.
Bad thing about Intel is that DDR5 is ludicrously expensive and not much faster than low latency DDR4. 13th gen should also support LGA1700 and DDR4 from the roadmaps, but Intel could change their mind. But, that means maybe a drop in upgrade later on for Intel. 5800X3D is the only one on the roadmap for AM4, and I suspect the 3D cache will be standard on AM5.