Hey, the 13600k is an absolute beast, its completely underestimated by so many, but the ones who did go for it have never complained or been disapointed, and neither will you. It's really nothing like what has tradationally been considered an i5 model, its gaming performance is almost spot on identical to the 12900k.
And most B760 boards will be perfectly fine, i like mini itx cases so i can only speak from my experience, but i originally put the 13600k in a Strix B660i and it was rock solid, so if your budget allows, i would try get a Strix B760 if you want something guaranteed.
Honestly, most haven’t said the way it is, the 14600k and its variants is a 13600k with an overclock, that’s all it is.
In your scenario, where you live, the 13600k costs more because it has the iGPU, which the 14600kf doesn’t.
As for gaming and bottlenecking, you can literally pair a 13600k with a 4090 and have minimal bottleneck when compared to a 13900k.
People still think of these as just i5’s but anyone who has one, will tell you they are way more powerful than what most have traditionally known as an i5.
No matter which way you look at it, there is always a bottleneck one way or another, there’s nothing you can do about that. But what you can do is try your best to ensure you’re more bottlenecked by the GPU, than you are CPU.
In the case of a 13600k/14600k/KF and a 3070 all the way up to about a 4070ti-4080, you will be GPU bottlenecked. So choose whichever suites your budget, either way you’re going to have one hell of a powerful CPU, just decide whether you want/need the iGPU or not.
I personally see the value in the iGPU myself, for that small bit extra in cost, it gives me piece of mind, knowing that if something happens to my GPU, I can still use the iGPU to have a display and troubleshoot, or at least still use the pc while the GPU is getting repaired or replaced.