### 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)

ClassDB::bind_method(D_METHOD("get_node_count"), &SceneState::get_node_count);
	ClassDB::bind_method(D_METHOD("get_node_type", "idx"), &SceneState::get_node_type);
	ClassDB::bind_method(D_METHOD("get_node_name", "idx"), &SceneState::get_node_name);
	ClassDB::bind_method(D_METHOD("get_node_path", "idx", "for_parent"), &SceneState::get_node_path, DEFVAL(false));
	ClassDB::bind_method(D_METHOD("get_node_owner_path", "idx"), &SceneState::get_node_owner_path);
	ClassDB::bind_method(D_METHOD("is_node_instance_placeholder", "idx"), &SceneState::is_node_instance_placeholder);
	ClassDB::bind_method(D_METHOD("get_node_instance_placeholder", "idx"), &SceneState::get_node_instance_placeholder);
	ClassDB::bind_method(D_METHOD("get_node_instance", "idx"), &SceneState::get_node_instance);
	ClassDB::bind_method(D_METHOD("get_node_groups", "idx"), &SceneState::_get_node_groups);
	ClassDB::bind_method(D_METHOD("get_node_index", "idx"), &SceneState::get_node_index);
	ClassDB::bind_method(D_METHOD("get_node_property_count", "idx"), &SceneState::get_node_property_count);
	ClassDB::bind_method(D_METHOD("get_node_property_name", "idx", "prop_idx"), &SceneState::get_node_property_name);
	ClassDB::bind_method(D_METHOD("get_node_property_value", "idx", "prop_idx"), &SceneState::get_node_property_value);
	ClassDB::bind_method(D_METHOD("get_connection_count"), &SceneState::get_connection_count);
	ClassDB::bind_method(D_METHOD("get_connection_source", "idx"), &SceneState::get_connection_source);
	ClassDB::bind_method(D_METHOD("get_connection_signal", "idx"), &SceneState::get_connection_signal);
	ClassDB::bind_method(D_METHOD("get_connection_target", "idx"), &SceneState::get_connection_target);
	ClassDB::bind_method(D_METHOD("get_connection_method", "idx"), &SceneState::get_connection_method);
	ClassDB::bind_method(D_METHOD("get_connection_flags", "idx"), &SceneState::get_connection_flags);
	ClassDB::bind_method(D_METHOD("get_connection_binds", "idx"), &SceneState::get_connection_binds);
	ClassDB::bind_method(D_METHOD("get_connection_unbinds", "idx"), &SceneState::get_connection_unbinds);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_DISABLED);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_INSTANCE);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_MAIN);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_MAIN_INHERITED);
}
SceneState::SceneState() {