### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

if (!dialog) {
		dialog = memnew(EditorFileDialog);
		dialog->connect("file_selected", callable_mp(this, &EditorPropertyPath::_path_selected));
		dialog->connect("dir_selected", callable_mp(this, &EditorPropertyPath::_path_selected));
		add_child(dialog);
	}
	String full_path = get_edited_property_value();
	dialog->clear_filters();
	if (global) {
		dialog->set_access(EditorFileDialog::ACCESS_FILESYSTEM);
	} else {
		dialog->set_access(EditorFileDialog::ACCESS_RESOURCES);
	}
	if (folder) {
		dialog->set_file_mode(EditorFileDialog::FILE_MODE_OPEN_DIR);
		dialog->set_current_dir(full_path);
	} else {
		dialog->set_file_mode(save_mode ? EditorFileDialog::FILE_MODE_SAVE_FILE : EditorFileDialog::FILE_MODE_OPEN_FILE);
		for (int i = 0; i < extensions.size(); i++) {
			String e = extensions[i].strip_edges();
			if (!e.is_empty()) {
				dialog->add_filter(extensions[i].strip_edges());
			}
		}
		dialog->set_current_path(full_path);
	}
	dialog->popup_file_dialog();
}
void EditorPropertyPath::update_property() {