### 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 (updating) {
		return;
	}
	Variant array = object->get_array().duplicate();
	array.call("resize", int(p_page));
	emit_changed(get_edited_property(), array, "", false);
	update_property();
}
void EditorPropertyArray::_add_element() {
	_length_changed(double(object->get_array().call("size")) + 1.0);
}
void EditorPropertyArray::setup(Variant::Type p_array_type, const String &p_hint_string) {
	array_type = p_array_type;
	
	
	if (!p_hint_string.is_empty()) {
		int hint_subtype_separator = p_hint_string.find(":");
		if (hint_subtype_separator >= 0) {
			String subtype_string = p_hint_string.substr(0, hint_subtype_separator);
			int slash_pos = subtype_string.find("/");
			if (slash_pos >= 0) {
				subtype_hint = PropertyHint(subtype_string.substr(slash_pos + 1, subtype_string.size() - slash_pos - 1).to_int());
				subtype_string = subtype_string.substr(0, slash_pos);
			}
			subtype_hint_string = p_hint_string.substr(hint_subtype_separator + 1, p_hint_string.size() - hint_subtype_separator - 1);
			subtype = Variant::Type(subtype_string.to_int());
		}
	}
}
void EditorPropertyArray::_reorder_button_gui_input(const Ref<InputEvent> &p_event) {