PS5 is not a bad shout if you're building a pc specifically for gaming.
Zen 3 Cpu plus motherboard/ram/nvme drive for storage is $1200-1300+. Cheapest of the latest gpus(3070) is $1150 locally or $850-900 imported. That's before psu, extra storage, case et al.
A $2k budget needs to wait for availability and prices to drop, or for the mid/lower range gpus to be released from amd/nvidia.
Current games are very keen on single core performance/clock speeds so changing thermal paste and Ocing the 6600k will get another 6 months out of it while you wait for either of the above to occur. Gpu is a more important indicator for gaming performance but that hasn't been mentioned by OP. Should still be able to play all his fav games on PC with current rig with a gentle oc.
PS5 digital version, if you can find one, does 4K 30\60 gaming for $650. Something my ryzen 3600 build from last year with a 1080ti would struggle with. If you're just interested in gaming, assuming you have a TV, that's incredible value to play games. Extra bonus if you're just a pc gamer, there's an immediate library of exceptional games to play available from the ps4 era too.