### 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.h"
#include "core/config/project_settings.h"
#include "core/core_string_names.h"
#include "editor/create_dialog.h"
#include "editor/editor_node.h"
#include "editor/editor_properties_array_dict.h"
#include "editor/editor_properties_vector.h"
#include "editor/editor_resource_picker.h"
#include "editor/editor_scale.h"
#include "editor/editor_settings.h"
#include "editor/gui/editor_file_dialog.h"
#include "editor/gui/editor_spin_slider.h"
#include "editor/gui/scene_tree_editor.h"
#include "editor/inspector_dock.h"
#include "editor/plugins/script_editor_plugin.h"
#include "editor/project_settings_editor.h"
#include "editor/property_selector.h"
#include "scene/2d/gpu_particles_2d.h"
#include "scene/3d/fog_volume.h"
#include "scene/3d/gpu_particles_3d.h"
#include "scene/gui/color_picker.h"
#include "scene/main/window.h"
#include "scene/resources/font.h"
#include "scene/resources/mesh.h"
#include "scene/resources/packed_scene.h"
void EditorPropertyNil::update_property() {