### 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)

EditorPropertyResource *editor = memnew(EditorPropertyResource);
				editor->setup(p_object, p_path, p_hint == PROPERTY_HINT_RESOURCE_TYPE ? p_hint_text : "Resource");
				if (p_hint == PROPERTY_HINT_RESOURCE_TYPE) {
					const PackedStringArray open_in_new_inspector = EDITOR_GET("interface/inspector/resources_to_open_in_new_inspector");
					for (const String &type : open_in_new_inspector) {
						for (int j = 0; j < p_hint_text.get_slice_count(","); j++) {
							const String inherits = p_hint_text.get_slicec(',', j);
							if (ClassDB::is_parent_class(inherits, type)) {
								editor->set_use_sub_inspector(false);
							}
						}
					}
				}
				return editor;
			}
		} break;
		case Variant::CALLABLE: {
			EditorPropertyCallable *editor = memnew(EditorPropertyCallable);
			return editor;
		} break;
		case Variant::SIGNAL: {
			EditorPropertySignal *editor = memnew(EditorPropertySignal);
			return editor;
		} break;
		case Variant::DICTIONARY: {
			if (p_hint == PROPERTY_HINT_LOCALIZABLE_STRING) {
				EditorPropertyLocalizableString *editor = memnew(EditorPropertyLocalizableString);
				return editor;
			} else {
				EditorPropertyDictionary *editor = memnew(EditorPropertyDictionary);