### 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)

return NodePath(".");
	}
	return NodePath(sub_path, false);
}
int SceneState::get_node_property_count(int p_idx) const {
	ERR_FAIL_INDEX_V(p_idx, nodes.size(), -1);
	return nodes[p_idx].properties.size();
}
StringName SceneState::get_node_property_name(int p_idx, int p_prop) const {
	ERR_FAIL_INDEX_V(p_idx, nodes.size(), StringName());
	ERR_FAIL_INDEX_V(p_prop, nodes[p_idx].properties.size(), StringName());
	return names[nodes[p_idx].properties[p_prop].name & FLAG_PROP_NAME_MASK];
}
Vector<String> SceneState::get_node_deferred_nodepath_properties(int p_idx) const {
	Vector<String> ret;
	ERR_FAIL_INDEX_V(p_idx, nodes.size(), ret);
	for (int i = 0; i < nodes[p_idx].properties.size(); i++) {
		uint32_t idx = nodes[p_idx].properties[i].name;
		if (idx & FLAG_PATH_PROPERTY_IS_NODE) {
			ret.push_back(names[idx & FLAG_PROP_NAME_MASK]);
		}
	}
	return ret;
}
Variant SceneState::get_node_property_value(int p_idx, int p_prop) const {
	ERR_FAIL_INDEX_V(p_idx, nodes.size(), Variant());
	ERR_FAIL_INDEX_V(p_prop, nodes[p_idx].properties.size(), Variant());
	return variants[nodes[p_idx].properties[p_prop].value];
}
NodePath SceneState::get_node_owner_path(int p_idx) const {