PySide6, QTreeWidget, showing full column text as tooltip if and only if the column text is truncated

Question

I created a simple table with QTreeWidget. When a column's text is too long for the column width, it gets truncated with ellipses. Can I show the full text when the user hovers the mouse over the column?

I have tried the following code, but I do not know how to get if the text is truncated or not. Also, the tooltip may not be reliably appearing.

import sys

from PySide6.QtWidgets import QApplication, QTreeWidget, QTreeWidgetItem

data = {
    "Dog": "The dog is a domesticated descendant of the wolf.",
    "Cat": "Meow!"}

app = QApplication(sys.argv)

tree = QTreeWidget()
tree.setMouseTracking(True)
tree.setColumnCount(2)
tree.setHeaderLabels(["Animal", "Description"])
tree.setColumnWidth(0, 100)
tree.setColumnWidth(1, 100)

items = []
for key, value in data.items():
    item = QTreeWidgetItem([key, value])
    items.append(item)

tree.insertTopLevelItems(0, items)

def show_tooltip(item, column):
    row = tree.indexOfTopLevelItem(item);
    print(f"mouse hover over {row}, {column}");
    if column == 1:
        isTruncated = True #Somehow get if the current column text is truncated.
        if isTruncated:
            tree.setToolTip("Show the full column text")
        else:
            tree.setToolTip("")

tree.itemEntered.connect(show_tooltip)

tree.show()
sys.exit(app.exec())