### 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)

src_id = FLAG_ID_IS_PATH | nodepath_map[p_node];
				} else {
					int sidx = nodepath_map.size();
					nodepath_map[p_node] = sidx;
					src_id = FLAG_ID_IS_PATH | sidx;
				}
			}
			int target_id;
			if (node_map.has(target)) {
				target_id = node_map[target];
			} else {
				if (nodepath_map.has(target)) {
					target_id = FLAG_ID_IS_PATH | nodepath_map[target];
				} else {
					int sidx = nodepath_map.size();
					nodepath_map[target] = sidx;
					target_id = FLAG_ID_IS_PATH | sidx;
				}
			}
			ConnectionData cd;
			cd.from = src_id;
			cd.to = target_id;
			cd.method = _nm_get_string(base_callable.get_method(), name_map);
			cd.signal = _nm_get_string(c.signal.get_name(), name_map);
			cd.flags = c.flags;
			cd.unbinds = unbinds;
			for (int i = 0; i < binds.size(); i++) {
				cd.binds.push_back(_vm_get_variant(binds[i], variant_map));
			}
			connections.push_back(cd);