### 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)

last_color = picker->get_pick_color();
}
void EditorPropertyColor::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_ENTER_TREE:
		case NOTIFICATION_THEME_CHANGED: {
			picker->set_custom_minimum_size(Size2(0, get_theme_constant(SNAME("color_picker_button_height"), SNAME("Editor"))));
		} break;
	}
}
void EditorPropertyColor::update_property() {
	picker->set_pick_color(get_edited_property_value());
	const Color color = picker->get_pick_color();
	
	if (picker->is_editing_alpha()) {
		picker->set_tooltip_text(vformat(
				"R: %s\nG: %s\nB: %s\nA: %s",
				rtos(color.r).pad_decimals(2),
				rtos(color.g).pad_decimals(2),
				rtos(color.b).pad_decimals(2),
				rtos(color.a).pad_decimals(2)));
	} else {
		picker->set_tooltip_text(vformat(
				"R: %s\nG: %s\nB: %s",
				rtos(color.r).pad_decimals(2),
				rtos(color.g).pad_decimals(2),
				rtos(color.b).pad_decimals(2)));
	}
}
void EditorPropertyColor::setup(bool p_show_alpha) {