### 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)

custom_value_edit->set_text(get_edited_property_value());
	edit_custom_layout->hide();
	default_layout->show();
}
void EditorPropertyTextEnum::update_property() {
	String current_value = get_edited_property_value();
	int default_option = options.find(current_value);
	
	if (loose_mode) {
		custom_value_edit->set_text(current_value);
		option_button->clear();
		
		if (default_option < 0 && !current_value.is_empty()) {
			option_button->add_item(current_value, options.size() + 1001);
			option_button->select(0);
			option_button->add_separator();
		}
		
		option_button->add_item("", options.size() + 1000);
		for (int i = 0; i < options.size(); i++) {
			option_button->add_item(options[i], i);
			if (options[i] == current_value) {
				option_button->select(option_button->get_item_count() - 1);
			}
		}
	} else {
		option_button->select(default_option);
	}
}
void EditorPropertyTextEnum::setup(const Vector<String> &p_options, bool p_string_name, bool p_loose_mode) {