### 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(), Ref<PackedScene>());
	if (nodes[p_idx].instance >= 0) {
		if (nodes[p_idx].instance & FLAG_INSTANCE_IS_PLACEHOLDER) {
			return Ref<PackedScene>();
		} else {
			return variants[nodes[p_idx].instance & FLAG_MASK];
		}
	} else if (nodes[p_idx].parent < 0 || nodes[p_idx].parent == NO_PARENT_SAVED) {
		if (base_scene_idx >= 0) {
			return variants[base_scene_idx];
		}
	}
	return Ref<PackedScene>();
}
String SceneState::get_node_instance_placeholder(int p_idx) const {
	ERR_FAIL_INDEX_V(p_idx, nodes.size(), String());
	if (nodes[p_idx].instance >= 0 && (nodes[p_idx].instance & FLAG_INSTANCE_IS_PLACEHOLDER)) {
		return variants[nodes[p_idx].instance & FLAG_MASK];
	}
	return String();
}
Vector<StringName> SceneState::get_node_groups(int p_idx) const {
	ERR_FAIL_INDEX_V(p_idx, nodes.size(), Vector<StringName>());
	Vector<StringName> groups;
	for (int i = 0; i < nodes[p_idx].groups.size(); i++) {
		groups.push_back(names[nodes[p_idx].groups[i]]);
	}
	return groups;
}
NodePath SceneState::get_node_path(int p_idx, bool p_for_parent) const {