Add a unit test for changing DirecotryTree.path

tests/directory_tree/test_change_path.py

@@ -0,0 +1,20 @@
+from pathlib import Path
+
+from textual.app import App, ComposeResult
+from textual.widgets import DirectoryTree
+
+
+class DirectoryTreeApp(App[None]):
+
+    def compose(self) -> ComposeResult:
+        yield DirectoryTree(".")
+
+
+async def test_change_directory_tree_path(tmpdir: Path) -> None:
+    """The DirectoryTree should react to the path changing."""
+
+    async with DirectoryTreeApp().run_test() as pilot:
+        assert pilot.app.query_one(DirectoryTree).root.data.path == Path(".")
+        pilot.app.query_one(DirectoryTree).path = tmpdir
+        await pilot.pause()
+        assert pilot.app.query_one(DirectoryTree).root.data.path == tmpdir