None of the above. Not even close. In 1080p maybe, since the gpu won't be doing much, but 4k is entirely different, literally 4x the amount of pixels to populate, which has nothing to do with the cpu, that's all gpu bound.
On top of that, Ampere is a new design where it offers direct rendering. Prior, the cpu needed to pre-render all game code, so set an fps limit by the amount of frames pre-rendered in a second. With Ampere cards, some of the graphics code is actually direct rendered by the gpu instead, decreasing reliance on the cpu, which gets bypassed and freed up to deal with the extras like physX and AI code.
All 7th, 8th,9th, 10th Gen cpus are basically nothing more than refinements on the 6th Gen Skylake cpus, so figure a 6700k with a 3070 is going to perform somewhat equitably to a 8700k and 2080ti. It'll just be a shift in performance.
No such thing as a cpu bottleneck. Even with Ampere cards, the cpu will still SET the fps limits. The gpu either lives up to that limit or fails. The cpu cannot Slow the flow of info, the definition of a bottleneck, as it is the Source of info. Depending on the game, detail settings, resolution the gpu will either be more capable, balanced or not able to equal the cpu.