The term 'bottlenecked' is often thrown about/misused so much as to lose any sense of meaning. Something is always limiting performance, be it GPU and/or CPU in varying degrees depending on resolution, visual quality/detail/filtering, the game, and monitor refresh rate, etc..
Certainly a faster processor like a 5800X would do even better with a better GPU than a 3060 but, not everyone has a 3080Ti or 3090, so, in that sense, nearly everyone is GPU-limited...; does that mean no one should upgrade processors save for those that have the very best GpUs? Of course not.
View: https://www.youtube.com/watch?v=_P_AGv-DJbU
Although the 2600X is not shown on the graph below, realize it won't be
that much below the 2700X which is shown in one game, and, although it's FPS might be sometimes only half that of the 12900K, 180 fps compared to 360 fps is hardly a 'slideshow' either...(and that difference would only be seen with the very best GPUs!)
If you are 'not unhappy'(i.e., semi-content!) with FPS, I'd wait for the next gen of both GPUs and AM5 and Intel's Comet Lake to hit....