If you have budget get 13700f. It will last 5 years atleast. 13400f is as fast as 5800x. It’s good but not excellent. You can also look into 12700f option much better than 13400f and mostly on sale

8f you can wait for 15th gen do it. Since 15th gen going to be on 7nm and it will be a big boost in performance.

That’s a big jump.

9600k is 6 core without ht and it stutters a lot. I shifted from the same to 5800x and it was a big difference. 8 core/16 threads brings smoothness. 6 threads is just too limited there.

However at 4k, the average fps will change very little however the smoothness of gameplay will change a lot.