### 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_COND_V(p_scene_state.is_null(), ERR_INVALID_PARAMETER);
	clear();
	for (const StringName &E : p_scene_state->names) {
		names.append(E);
	}
	for (const Variant &E : p_scene_state->variants) {
		variants.append(E);
	}
	for (const SceneState::NodeData &E : p_scene_state->nodes) {
		nodes.append(E);
	}
	for (const SceneState::ConnectionData &E : p_scene_state->connections) {
		connections.append(E);
	}
	for (KeyValue<NodePath, int> &E : p_scene_state->node_path_cache) {
		node_path_cache.insert(E.key, E.value);
	}
	for (const NodePath &E : p_scene_state->node_paths) {
		node_paths.append(E);
	}
	for (const NodePath &E : p_scene_state->editable_instances) {
		editable_instances.append(E);
	}
	base_scene_idx = p_scene_state->base_scene_idx;
	return OK;
}
Ref<SceneState> SceneState::get_base_scene_state() const {