I have the 13600KF and it runs my 4090 sweet. 5.5ghz P-Cores 4.1 E-Cores. 13700K gives you a couple extra p-cores which may be nice to have later on.

My 4090 would disagree with you! 13600kf here (edit) it’s got 6 pcores

Yep I have a 240 Lianli Galahad + 13600kf. Overclocked undervolted never seen temps above 75c. I do run the fan on max though. If your case can fit a 360mm I would do that just for lower fan speeds/noise.