The widget will output the new, edited dataframe. However, if you want to get the edited dataframe from Session State, you’ll have to apply the edits to your original dataframe yourself. (Loop through each of the edits, deletions, and additions and apply the change to your original dataframe.)
So generally speaking, if you want to work with the edited dataframe, get it from the widget output instead of Session State.
Here is an example of working with the edits (and even updating another column as a result of the edit): Data Editor Checkbox on Change - #2 by mathcatsand