That has not been my experience, although I may be doing the multiple levels differently to how you are, but mine are working in the 3rd level as per your picture. The widget I use and works, is in the marketplace called camera mp4 history
if you wish to look and play with its code. I define the variable in the widget and only use defaultValue to set the value, not create the variables. I use multiple widgets all on the same page and they do not share a GLOBAL variable, but unique separate variables that all work as intended in each widget. The defaultValue appears to just set all variables in the page with the given name. If you are not defining the variable in the widget, then this may be the reason it works for me and not for you.
I am not an expert and don’t know if this is the wrong way, but it works for me and hope it can help you. Hopefully someone with some time to donate can: 1. document this. 2. Request a way to do it at the widget level with a github issue as clearly multiple people are wanting this.