### 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)

ERR_FAIL_INDEX_V(p_idx, nodes.size(), NodePath());
	if (nodes[p_idx].owner < 0 || nodes[p_idx].owner == NO_PARENT_SAVED) {
		return NodePath(); 
	}
	if (nodes[p_idx].owner & FLAG_ID_IS_PATH) {
		return node_paths[nodes[p_idx].owner & FLAG_MASK];
	} else {
		return get_node_path(nodes[p_idx].owner & FLAG_MASK);
	}
}
int SceneState::get_connection_count() const {
	return connections.size();
}
NodePath SceneState::get_connection_source(int p_idx) const {
	ERR_FAIL_INDEX_V(p_idx, connections.size(), NodePath());
	if (connections[p_idx].from & FLAG_ID_IS_PATH) {
		return node_paths[connections[p_idx].from & FLAG_MASK];
	} else {
		return get_node_path(connections[p_idx].from & FLAG_MASK);
	}
}
StringName SceneState::get_connection_signal(int p_idx) const {
	ERR_FAIL_INDEX_V(p_idx, connections.size(), StringName());
	return names[connections[p_idx].signal];
}
NodePath SceneState::get_connection_target(int p_idx) const {