[2023] Cooldown recovery interaction question

Guys, could you tell me please, does cooldown recovery speed modifiers affect such things like Freezing Cascade cooldown?

If yes - where I can see the result cooldown? Because I have some recovery speed mods on gear, but on skill tree it still shows the initial value of 5

https://preview.redd.it/py38zy0gj7ab1.png?width=1339&format=png&auto=webp&v=enabled&s=1265bc5feee2a7212e6f509b432efaa81293cf72