### 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)

NodePath p;
	if (pointer_mode) {
		p = get_edited_object()->get(_get_meta_pointer_property());
	} else {
		p = get_edited_property_value();
	}
	assign->set_tooltip_text(p);
	if (p == NodePath()) {
		assign->set_icon(Ref<Texture2D>());
		assign->set_text(TTR("Assign..."));
		assign->set_flat(false);
		return;
	}
	assign->set_flat(true);
	Node *base_node = nullptr;
	if (base_hint != NodePath()) {
		if (get_tree()->get_root()->has_node(base_hint)) {
			base_node = get_tree()->get_root()->get_node(base_hint);
		}
	} else {
		base_node = Object::cast_to<Node>(get_edited_object());
	}
	if (!base_node || !base_node->has_node(p)) {