WinForms Tabbed Interface configured as Tree of Tabs

I have a WinForms project where the Form has a bunch of tabs configured something like this:
Here the user has selected "tabPage1", and within that TabPage they selected "tabPage4", and within that TabPage they selected "tabPgae12".

Now I want a textBox at the bottom that displays which innermost tab has been selected. (i.e. tabPage12 in the image above.)

I'm thinking the tabs really form a tree like structure:
I'm wondering if I should somehow place the tabs in a tree like data structure. Would that help me figure out which tab is the selected in the tree?

WinForms (at least as this project is currently configured) doesn't seem to have nice separation of View. Is there a design pattern that will give us better separation of View for WinForms?

Is there a clean way to design this program?

Currently it seems like I would have to manually sift through all the tabs, figure out which tab {1,2} is selected, then based on that figure out which tab {3,4,5} is selected, then based on that figure out which tab {10,11,12,13} is selected. Crawling through the View like that seems tedious and wrong. Is there a better way the TextBox at the bottom can figure out which tab is selected and display that number?