Ensure the Tree's internal tracker gets updated on node delete

See #2462.

src/textual/widgets/_tree.py

@@ -352,6 +352,18 @@ class TreeNode(Generic[TreeDataType]):
     class RemoveRootError(Exception):
         """Exception raised when trying to remove a tree's root node."""
 
+    def _remove(self) -> None:
+        """Remove the current node and all its children.
+
+        Note:
+            This is the internal support method for `remove`.
+        """
+        for child in reversed(self._children):
+            child._remove()
+        assert self._parent is not None
+        del self._parent._children[self._parent._children.index(self)]
+        del self._tree._tree_nodes[self.id]
+
     def remove(self) -> None:
         """Remove this node from the tree.
 
@@ -360,8 +372,7 @@ class TreeNode(Generic[TreeDataType]):
         """
         if self.is_root:
             raise self.RemoveRootError("Attempt to remove the root node of a Tree.")
-        assert self._parent is not None
+        self._remove()
-        del self._parent._children[self._parent._children.index(self)]
         self._tree._invalidate()