### Godot version

4.1.dev4

### System information

Windows 10 Godot 4.1.dev4

### Issue description

The watched property in the Multiplayer Synchronizer node is supposed to pass the variable through the network only when it changes, but as I use the network profiler, it is evidently not working as intended

### Steps to reproduce

Open 2 debug instances on the project I will give, use the network profiler and you will see the variable does not change, although it goes up to 780b/s on the network

### Minimal reproduction project

[minimalproject.zip](https://github.com/godotengine/godot/files/11659414/minimalproject.zip)

_add_pressed();
}
void ReplicationEditor::_tree_item_edited() {
	TreeItem *ti = tree->get_edited();
	if (!ti || config.is_null()) {
		return;
	}
	int column = tree->get_edited_column();
	ERR_FAIL_COND(column < 1 || column > 3);
	const NodePath prop = ti->get_metadata(0);
	EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
	bool value = ti->is_checked(column);
	
	if (column == 3 && value && config->get_watch_properties().size() > 64) {
		error_dialog->set_text(TTR("Each MultiplayerSynchronizer can have no more than 64 watched properties."));
		error_dialog->popup_centered();
		ti->set_checked(column, false);
		return;
	}
	String method;
	if (column == 1) {