### 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_MSG(node_path_cache.size() == 0, -1, "This operation requires the node cache to have been built.");
	if (!node_path_cache.has(p_node)) {
		if (get_base_scene_state().is_valid()) {
			int idx = get_base_scene_state()->find_node_by_path(p_node);
			if (idx != -1) {
				int rkey = _find_base_scene_node_remap_key(idx);
				if (rkey == -1) {
					rkey = nodes.size() + base_scene_node_remap.size();
					base_scene_node_remap[rkey] = idx;
				}
				return rkey;
			}
		}
		return -1;
	}
	int nid = node_path_cache[p_node];
	if (get_base_scene_state().is_valid() && !base_scene_node_remap.has(nid)) {
		
		
		
		int idx = get_base_scene_state()->find_node_by_path(p_node);
		if (idx != -1) {
			base_scene_node_remap[nid] = idx;
		}
	}
	return nid;
}
int SceneState::_find_base_scene_node_remap_key(int p_idx) const {