If you are looking to manually backup your data using a file manager app, you need to know where the local files reside. On Android, security restrictions (introduced heavily in Android 11, 12, 13, and 14) make accessing these folders slightly more difficult, but they can still be reached using specialized file explorers like ZArchiver or via a PC connection.
If the game fails to recognize your backup or gives an error when attempting to connect to Google Play Games, try these steps: Save Data Monster Hunter Stories Android