Hi, in my current PC i have an RX 580 8gb, Ryzen 5 2600 and 32gb of RAM 3000mhz CL 16 (its 3200mhz but i had stability issues and had to put them at 3000).

I recently bought a 165hz monitor but i struggle to reach that fps in CS2, which is the main game i play. I read that its a CPU game, so i guess its time to update the 2600.
My goal is basically reaching around the 165-200 fps line in CS2 to benefit from the monitor with the least money possible, but if i get a CPU that will future-proof my build for some years i won't complain. (mind that i basically never play very demanding games, and when i do i don't have problems favouring fps over graphics, after all the monitor is a TN haha)

Reading around i stumbled across the 5 5600x (read also a lot about the 5700x3d but its 150 euro more so no thanks) or the 5700x. (if you have other things in mind suggest freely im open to anything)

So my question is which one should i buy and at which price? After a very quick search the 5600x is around 105€ and the 5700x 115€.
Also, will the GPU bottleneck be a big problem?
Btw i'll run memtest86 to check if the RAM is faulty cause i was on 3000mhz for years but i feel like if i upgrade the CPU i should at least max the ram frequency.