Your gaming performance will primarily be gated by the graphics card, not the cpu.
Particularly at resolutions higher than 1080P
Most any current gen processor in the $300 price range will usually do the job.
Most games can not effectively use more than 6 threads.
It is more important that the threads be fast.
If you are looking at a 16 thread processor like the 5800x or the 11700K. the single thread passmark rating of each is about 3500.
The 5950 has the same 3500 but with 32 threads.
If you play multiplayer games with many participants, then more threads can help.
Or if you are concurrently multitasking, more threads help.
As to overclocking is is no longer a way to get something for nothing.
Processors are binned and come performing to their max using various turbo mechanisms. That increases the performance of a few cores when needed and conditions permit. The value of the 16 thread i9-11900K is that it is better binned with a better turbo and a single thread rating around 3700
The value in overclocking comes when you can raise the performance of all cores so that multithreaded apps that can use all cores can perform better.
Read this review of the $200 i5-11400.
Look at the ten game average results.
The Core i5-11400F coupled with a B560 motherboard make for an interesting build configuration, as it's significantly cheaper than the Core i5-11600K/Z590 and less than the cost...
www.techspot.com
If you have no budget restrictions, by all means buy the best. 5959x or i9-11900K
And, be prepared to see that whatever you buy today will be old hat in a year or two when new processors,motherboards, and ddr5 ram arrive.