If I was you and dead set on upgrading, the only thing I’d upgrade to is either the 13700k or 14700k since it has more P-cores which will help with gaming, but it probably will be negligible in most games at your resolution. The 13600k/13700k/14600k/14700k also comes with more e-cores (IIRC) but they won’t really make that big of an impact in gaming.
Honestly, I’d just OC the 12600k you have and call it a day if you’re gaming at 4k since you’re mostly going to be bottlenecked at the GPU.
If I was you and dead set on upgrading, the only thing I’d upgrade to is either the 13700k or 14700k since it has more P-cores which will help with gaming, but it probably will be negligible in most games at your resolution. The 13600k/13700k/14600k/14700k also comes with more e-cores (IIRC) but they won’t really make that big of an impact in gaming.
Honestly, I’d just OC the 12600k you have and call it a day if you’re gaming at 4k since you’re mostly going to be bottlenecked at the GPU.