I dont think you will lose that much on PCIe gen 3 vs. 4. However , that Cpu will be a bottleneck.
9700K might have 8 cores, but i lags hyper threading. So it is only a 8 thread cpu. Some games needs more than 8 threads. I have seen this CPU peak at 100 % load with slower Gpu.
I dont have a 4080, but i do have a 4090 and for that GPU, even my not that old Ryzen 9 5950X can be a botleneck for my 4090.
I dont know what resolution you play in. But to get full advantage of 4080.
I will strongly advise to get a CPU with 12 threads or more. Meaning 6 cores/12 thread or idealy 8 cores/16 threads.
I am not sure you can get a away just upgrading to a I9 9900K and overclock it. It´s still a CPU from 2018.
I will strongly advice to upgrade to either of these CPU depending on your econemy and needs.
From AMD at least 5800X and even better 5800X3D or Zen 7800X (you might want to wait and se what zen 4 3D chips can do)
From intel 12600K or better yet 12700K or there newest 13 gen 13600K or 13700K. The none K is also a good choise, but they are locked and cant be overclock and runs at lover clockspeed than K models. So they might be cheaper, but also slower than the K models.