Well, with latest BIOS update, version F27, you can also go with 14th gen Intel CPU. E.g i5-14400.
With i5-13600K, you have to buy aftermarket CPU cooler as well since CPU doesn't come with one. And stock Intel cooler on your i5-12400F isn't sufficient enough.
E.g Thermalright Peerless Assassin 120 SE (king of air coolers), IF your PC case has CPU cooler clearance at least 155mm;
specs:
https://www.thermalright.com/product/peerless-assassin-120-se/
New PSU is also needed. What you have, is low quality PSU. And since PSU powers everything, it is
the most important component inside the PC.
For RTX 4070, you're looking towards 750W, good quality unit. E.g Seasonic Focus/Vertex/PRIME or Corsair RMx/RMi/HXi/AXi or Super Flower Leadex Gold/Platinum/Titanium.
For 2nd opinion about your PSU, look it from PSU tier list,
link:
https://forums.tomshardware.com/thr...er-list-rev-14-8-final-update-jul-21.3624094/
You can find it under Tier C, while those that i suggested, are all Tier A.
(My 3x PCs are all powered by Tier A Seasonic units as well. Full specs with pics in my sig.)
Easy to test out.
Reduce the resolution or graphical levels in the game and look if you can get more FPS.
If you do, then you're held back by GPU (since lesser load on GPU gives more FPS).
If you do not and FPS remains mostly the same, then you're held back by CPU and new CPU gives more FPS.