How to make a variable "public" and editable when the eye icon next to it does nothing when i'm clicking on it ?

So I encountered the same issue in 5.5, and it was not the expected behavior from the previous versions. I had been doing editor style widgets since 4.26 for various work and job positions since then and you could in the past edit the default value on creation through the event graph. Now it requires a little extra step where you read the default value and set it upon creation if it is not your intended value. A lot of my UI’s deal with accessing properties of multiple actors, or tagging selected actors in the viewport and accessing common properties to be used by non-UE users in my workplace, allowing them to adjust values on post process volumes, cameras, lights and materials on live shoots.

Solution again:

read the value and set the value from the control on the graph by dragging set or get value nodes from their respective widget controls.

Hope this helped someone.