### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
switch (tool_menu->get_item_id(p_idx)) {
		case TOOLS_ORPHAN_RESOURCES: {
			orphan_resources->show();
		} break;
		case TOOLS_SURFACE_UPGRADE: {
			surface_upgrade_dialog->popup_on_demand();
		} break;
		case TOOLS_CUSTOM: {
			if (tool_menu->get_item_submenu(p_idx) == "") {
				Callable callback = tool_menu->get_item_metadata(p_idx);
				Callable::CallError ce;
				Variant result;
				callback.callp(nullptr, 0, result, ce);
				if (ce.error != Callable::CallError::CALL_OK) {
					String err = Variant::get_callable_error_text(callback, nullptr, 0, ce);
					ERR_PRINT("Error calling function from tool menu: " + err);
				}
			} 
		} break;
	}
}
void EditorNode::_export_as_menu_option(int p_idx) {