How can I disaggregate the impact of a group of variables using machine learning?

I have a problem where the target variable Y (continuous, values: 0-1) is controlled by large number of variables. These variables can be grouped by the nature of the data:

Group 1 - x1, x2, x3, x4 
Group 2 - x5, x6, x7
Group 3 - x8, x9, x10, x12

After modeling Y~X, I would like to disaggregate the impact of these groups.

Example, I want to have a plot like this famous Hawkins and Sutton plot of climate change impacts.

But instead of time, I will have Y values from 0-1, and then I will have the impact of these 3 groups of explanatory variables in place of the three uncertainties shown in the plot.

How can I approach this in a tree-based or another ML model? Perhaps I don't know the right keywords to search for it.