### 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)

Transform2D val = get_edited_property_value();
	setting = true;
	spin[0]->set_value(val[0][0]);
	spin[1]->set_value(val[1][0]);
	spin[2]->set_value(val[2][0]);
	spin[3]->set_value(val[0][1]);
	spin[4]->set_value(val[1][1]);
	spin[5]->set_value(val[2][1]);
	setting = false;
}
void EditorPropertyTransform2D::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_ENTER_TREE:
		case NOTIFICATION_THEME_CHANGED: {
			const Color *colors = _get_property_colors();
			for (int i = 0; i < 6; i++) {
				
				if (i % 3 == 2) {
					spin[i]->add_theme_color_override("label_color", colors[3]);
				} else {
					spin[i]->add_theme_color_override("label_color", colors[i % 3]);
				}
			}
		} break;
	}
}
void EditorPropertyTransform2D::_bind_methods() {