### 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)

}
EditorPropertyNodePath::EditorPropertyNodePath() {
	HBoxContainer *hbc = memnew(HBoxContainer);
	hbc->add_theme_constant_override("separation", 0);
	add_child(hbc);
	assign = memnew(Button);
	assign->set_flat(true);
	assign->set_h_size_flags(SIZE_EXPAND_FILL);
	assign->set_clip_text(true);
	assign->set_auto_translate(false);
	assign->connect("pressed", callable_mp(this, &EditorPropertyNodePath::_node_assign));
	SET_DRAG_FORWARDING_CD(assign, EditorPropertyNodePath);
	hbc->add_child(assign);
	clear = memnew(Button);
	clear->set_flat(true);
	clear->connect("pressed", callable_mp(this, &EditorPropertyNodePath::_node_clear));
	hbc->add_child(clear);
	scene_tree = nullptr; 
}
void EditorPropertyRID::update_property() {
	RID rid = get_edited_property_value();
	if (rid.is_valid()) {
		uint64_t id = rid.get_id();
		label->set_text("RID: " + uitos(id));
	} else {
		label->set_text(TTR("Invalid RID"));
	}
}
EditorPropertyRID::EditorPropertyRID() {