### 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)

Ref<SceneState> ss = this;
	do {
		for (int i = 0; i < ss->connections.size(); i++) {
			const ConnectionData &c = ss->connections[i];
			NodePath np_from;
			if (c.from & FLAG_ID_IS_PATH) {
				np_from = ss->node_paths[c.from & FLAG_MASK];
			} else {
				np_from = ss->get_node_path(c.from);
			}
			NodePath np_to;
			if (c.to & FLAG_ID_IS_PATH) {
				np_to = ss->node_paths[c.to & FLAG_MASK];
			} else {
				np_to = ss->get_node_path(c.to);
			}
			StringName sn_signal = ss->names[c.signal];
			StringName sn_method = ss->names[c.method];
			if (np_from == p_node_from && sn_signal == p_signal && np_to == p_node_to && sn_method == p_method) {
				return true;
			}
		}
		if (p_no_inheritance) {
			break;
		}
		ss = ss->get_base_scene_state();