### 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 (!p_property.begins_with("indices") && !p_property.begins_with(PackedScene::META_POINTER_PROPERTY_BASE + "indices")) {
		return;
	}
	int index;
	if (p_property.begins_with("metadata/")) {
		index = p_property.get_slice("/", 2).to_int();
	} else {
		index = p_property.get_slice("/", 1).to_int();
	}
	Variant array;
	const Variant &original_array = object->get_array();
	if (original_array.get_type() == Variant::ARRAY) {
		
		Array temp;
		temp.assign(original_array.duplicate());
		array = temp;
	} else {
		array = original_array.duplicate();
	}
	array.set(index, p_value);
	object->set_array(array);
	emit_changed(get_edited_property(), array, "", true);
}
void EditorPropertyArray::_change_type(Object *p_button, int p_index) {