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On my computer (Windows 10, screen resolution 3000 x 2000, scaling of text and other elements set at 200% as the recommended value), the path browser is essentially unusable as the items overlap each other. See the attached image. 
I found that changing the following:
 def draw(self, x, y):
 # XXX This hard-codes too many geometry constants!
 dy = 40 # changed from 20
in tree.py solved the problem.

Another reason to replace IDLE's custom tree widget with hard-coded constants with ttk.Treeview.
I am closing this because I believe that #31552 will solve this problem. For an initial check, run the following test code, extracted from
https://tkdocs.com/tutorial/tree.html
Click the [+] buttons. I am curious whether commenting out the fix_scaling call makes any difference.
---------
import tkinter as tk
from tkinter import ttk
from idlelib.run import fix_scaling
root = tk.Tk()
tree = ttk.Treeview(root)
tree.pack()
fix_scaling(root)
tree.insert('', 'end', 'widgets', text='Widget Tour')
tree.insert('', 0, 'gallery', text='Applications')
id = tree.insert('', 'end', text='Tutorial')
tree.insert('widgets', 'end', text='Canvas')
tree.insert(id, 'end', text='Tree')
root.mainloop()

I ran the example you gave and it worked perfectly.