The Ryzen 5 2600x is 112% faster than the A10 7700K. More than double the speed. Your R7 260X will be able to put down all of its power, which is actually pretty good performance, and while you might have been getting everything you can out of it before, the CPU behind it makes a big difference too.
Bottlenecks are kind of a strange beast. If you get them the right way you don't notice them at all. The bottlenecks you notice are the bad ones. With a 2600x and an R7 260X you'll have a graphical bottleneck, but you won't notice it at all. You'll have smooth gameplay and great performance in many games. If you were to run the A10 with the 1060 you'd still be able to play games, but you won't be getting the most out of your video card, and any situation that is not optimal for the video card is not optimal for gaming.