### 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)

#include "editor_properties_array_dict.h"
#include "core/input/input.h"
#include "core/io/marshalls.h"
#include "editor/editor_properties.h"
#include "editor/editor_properties_vector.h"
#include "editor/editor_scale.h"
#include "editor/editor_settings.h"
#include "editor/gui/editor_spin_slider.h"
#include "editor/inspector_dock.h"
#include "scene/gui/button.h"
#include "scene/resources/packed_scene.h"
bool EditorPropertyArrayObject::_set(const StringName &p_name, const Variant &p_value) {
	String name = p_name;
	if (!name.begins_with("indices") && !name.begins_with(PackedScene::META_POINTER_PROPERTY_BASE + "indices")) {
		return false;
	}
	int index;
	if (name.begins_with("metadata/")) {
		index = name.get_slice("/", 2).to_int();
	} else {
		index = name.get_slice("/", 1).to_int();
	}
	array.set(index, p_value);
	return true;
}
bool EditorPropertyArrayObject::_get(const StringName &p_name, Variant &r_ret) const {