Most game settings have little impact on cpu usage. For example 60fp at 1080p will take about the same cpu work as 60fps at 4K. The extra work is on the gpu. As I said earlier, the cpu determines the best FPS, the gpu determines at what resolution and game settings you can achieve that FPS at. You can still achieve the FPS you get today with a 580, just you will be able to turn up game settings while getting that FPS.
This is fully true and why we keep noting that you may be overly concerned about the required strength of the CPU -- the more in game and gpu driver details you add (with maybe a couple exceptions), the lower the demand is on the CPU because your framerate drops ... at a 60 FPS cap, the load on the CPU will be roughly the same regardless of GPU/game settings - those don't really factor into CPU usage except that as you crankl the visual quality, the FPS drops, and the load on the CPU is generally reduced.
A r5 2600x will never ever bottleneck in your stated gaming scenarios, but if you can snag a 1600x for cheap and a cheap b450 mobo, that will also work just fine. On the Intel side a 9400F would be roughly same price and net you decent performance as well.
But I really think you are making grander assumptions about the potential of CPU bottlneck with FPS at 60 being the max you can display anyway - even if you did hit some CPU bottleneck (say if you kept the Xeon), there probably would be very little impact to your experience.
I know everyone is always going on about how easy you hit CPU bottlenecks and that you need the "best" gaming processor to avoid them or you'll die, but in reality this is really only ever a concern with a 2080ti and high refresh gaming. Neither of which applies to you.
Intel has a very powerful marketing capability and most of this that you hear around the web is all just parroting their marketing, without any real understanding of when a CPU is bottlnecking your game, when it even matters, and the final impact on your experience.
To throw some more Intel options out there, I agree with Sizzling that a 6700k or 7700k will be perfectly good as well if you can find them, maybe used?
I am also of the opinion that that bottlneck calculator is a bit like a fortune teller. There isn't nearly enough inputs for it to be able to do any accurate calculation - I assume it would represent the absolute worst case scenario - which would be high refresh gaming (144hz+) on medium or low game settings, but again, that doesn't apply to you.