Personally, I wouldn't do it if I already have a 12700K, but the 13600K is a bit faster than the 12700K. I myself own the 13600k and am satisfied myself, but I also switched from the i7 first generation to the 13th generation.

I wouldn't make the change either. It should also be clarified whether your mainboard can carry out the BIOS update for the 13th generation. If you are bored with the i7 12700k, I recommend overclocking it, provided the cooling is right and the Z690 chipset is available.

I don't think it makes sense. The performance difference is 10-15% ... Buying a whole new processor for that ... the 10-15% would have to be really important. And in that case I would switch directly to i9.