### 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)

switch (p_what) {
		case NOTIFICATION_ENTER_TREE:
		case EditorSettings::NOTIFICATION_EDITOR_SETTINGS_CHANGED: {
			add_theme_style_override("panel", EditorNode::get_singleton()->get_gui_base()->get_theme_stylebox(SNAME("panel"), SNAME("Panel")));
			add_pick_button->set_icon(get_theme_icon(SNAME("Add"), SNAME("EditorIcons")));
			pin->set_icon(get_theme_icon(SNAME("Pin"), SNAME("EditorIcons")));
		} break;
	}
}
void ReplicationEditor::_add_pressed() {