### 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(p_node, nodes.size());
	ERR_FAIL_INDEX(p_name, names.size());
	ERR_FAIL_INDEX(p_value, variants.size());
	NodeData::Property prop;
	prop.name = p_name;
	if (p_deferred_node_path) {
		prop.name |= FLAG_PATH_PROPERTY_IS_NODE;
	}
	prop.value = p_value;
	nodes.write[p_node].properties.push_back(prop);
}
void SceneState::add_node_group(int p_node, int p_group) {
	ERR_FAIL_INDEX(p_node, nodes.size());
	ERR_FAIL_INDEX(p_group, names.size());
	nodes.write[p_node].groups.push_back(p_group);
}
void SceneState::set_base_scene(int p_idx) {
	ERR_FAIL_INDEX(p_idx, variants.size());
	base_scene_idx = p_idx;
}
void SceneState::add_connection(int p_from, int p_to, int p_signal, int p_method, int p_flags, int p_unbinds, const Vector<int> &p_binds) {