Every individual will have to make the critical cost/performance ratio evaluation as to whether or not that last bit of performance bump possible from having the 'fastest processor available' is worth it, be it a 7800X3D or 13900K, is worth the added expense or not.
Some games scale better than others with CPU, while others are mostly GPU limited, with many games scaling modestly with increases in either.
It's a very tough call to make sometimes when pondering forking out money for a new mainboard, CPU, RAM, and GPU!
Personally, I like to get 'close to 90%' of top end CPU performance for 50% on the dollar when possible, so that a 'very good' mainboard/CPU combo purchased now is 'good enough' for gaming for 4-6 years , with perhaps only a GPU upgrade done at the 2-3 year point...
As to the rig mentioned, a 7700XCPU and /7800XT or 7900XT GPU combo would likely easily fulfill most folks needs...mine included.
Good luck with your upcoming decisions!