### 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)

Vector<Variant> binds;
			if (c.binds.size()) {
				binds.resize(c.binds.size());
				for (int j = 0; j < c.binds.size(); j++) {
					binds.write[j] = props[c.binds[j]];
				}
			}
			const Variant **argptrs = (const Variant **)alloca(sizeof(Variant *) * binds.size());
			for (int j = 0; j < binds.size(); j++) {
				argptrs[j] = &binds[j];
			}
			callable = callable.bindp(argptrs, binds.size());
		}
		cfrom->connect(snames[c.signal], callable, CONNECT_PERSIST | c.flags | (p_edit_state == GEN_EDIT_STATE_MAIN ? 0 : CONNECT_INHERITED));
	}
	
	
	while (stray_instances.size()) {
		memdelete(stray_instances.front()->get());
		stray_instances.pop_front();
	}
	for (int i = 0; i < editable_instances.size(); i++) {
		Node *ei = ret_nodes[0]->get_node_or_null(editable_instances[i]);
		if (ei) {
			ret_nodes[0]->set_editable_instance(ei, true);
		}
	}
	return ret_nodes[0];
}
static int _nm_get_string(const String &p_string, HashMap<StringName, int> &name_map) {