### 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)

array.push_back(other);
			} else {
				array.set(index, other);
			}
			dnp.base->set(base_property, array);
		} else {
			dnp.base->set(dnp.property, other);
		}
	}
	for (KeyValue<Ref<Resource>, Ref<Resource>> &E : resources_local_to_scene) {
		if (E.value->get_local_scene() == ret_nodes[0]) {
			E.value->setup_local_to_scene();
		}
	}
	
	int cc = connections.size();
	const ConnectionData *cdata = connections.ptr();
	for (int i = 0; i < cc; i++) {
		const ConnectionData &c = cdata[i];
		
		
		NODE_FROM_ID(cfrom, c.from);
		NODE_FROM_ID(cto, c.to);
		if (!cfrom || !cto) {
			continue;
		}
		Callable callable(cto, snames[c.method]);
		if (c.unbinds > 0) {
			callable = callable.unbind(c.unbinds);
		} else if (!c.binds.is_empty()) {