### 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)

new_item_key = p_new_item;
}
Variant EditorPropertyDictionaryObject::get_new_item_key() {
	return new_item_key;
}
void EditorPropertyDictionaryObject::set_new_item_value(const Variant &p_new_item) {
	new_item_value = p_new_item;
}
Variant EditorPropertyDictionaryObject::get_new_item_value() {
	return new_item_value;
}
EditorPropertyDictionaryObject::EditorPropertyDictionaryObject() {
}
void EditorPropertyArray::initialize_array(Variant &p_array) {
	if (array_type == Variant::ARRAY && subtype != Variant::NIL) {
		Array array;
		StringName subtype_class;
		Ref<Script> subtype_script;
		if (subtype == Variant::OBJECT && !subtype_hint_string.is_empty()) {
			if (ClassDB::class_exists(subtype_hint_string)) {
				subtype_class = subtype_hint_string;
			}
		}
		array.set_typed(subtype, subtype_class, subtype_script);
		p_array = array;
	} else {
		VariantInternal::initialize(&p_array, array_type);
	}
}
void EditorPropertyArray::_property_changed(const String &p_property, Variant p_value, const String &p_name, bool p_changing) {