### 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)

prop = memnew(EditorPropertyColor);
				} break;
				case Variant::STRING_NAME: {
					EditorPropertyText *ept = memnew(EditorPropertyText);
					ept->set_string_name(true);
					prop = ept;
				} break;
				case Variant::NODE_PATH: {
					prop = memnew(EditorPropertyNodePath);
				} break;
				case Variant::RID: {
					prop = memnew(EditorPropertyRID);
				} break;
				case Variant::SIGNAL: {
					prop = memnew(EditorPropertySignal);
				} break;
				case Variant::CALLABLE: {
					prop = memnew(EditorPropertyCallable);
				} break;
				case Variant::OBJECT: {
					if (Object::cast_to<EncodedObjectAsID>(value)) {
						EditorPropertyObjectID *editor = memnew(EditorPropertyObjectID);
						editor->setup("Object");
						prop = editor;
					} else {
						EditorPropertyResource *editor = memnew(EditorPropertyResource);
						editor->setup(object.ptr(), prop_name, "Resource");
						editor->set_use_folding(is_using_folding());
						prop = editor;
					}