### 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)

emit_signal(SNAME("object_id_selected"), p_property, p_id);
}
void EditorPropertyArray::update_property() {
	Variant array = get_edited_property_value();
	String array_type_name = Variant::get_type_name(array_type);
	if (array_type == Variant::ARRAY && subtype != Variant::NIL) {
		String type_name;
		if (subtype == Variant::OBJECT && (subtype_hint == PROPERTY_HINT_RESOURCE_TYPE || subtype_hint == PROPERTY_HINT_NODE_TYPE)) {
			type_name = subtype_hint_string;
		} else {
			type_name = Variant::get_type_name(subtype);
		}
		array_type_name = vformat("%s[%s]", array_type_name, type_name);
	}
	if (array.get_type() == Variant::NIL) {
		edit->set_text(vformat(TTR("(Nil) %s"), array_type_name));
		edit->set_pressed(false);
		if (container) {
			set_bottom_editor(nullptr);
			memdelete(container);
			button_add_item = nullptr;