Here’s the difference between the option [Auto] and [on].
If you have the Power Saving set to [on], it will still go into sleep mode even if it's connected to a power source. If you choose [auto], your camera will stay online when it's plugged in. When you find yourself in a tough spot, with only one power bank as your power source, [on] will be your best bet. It helps conserve your battery life as much as possible.
On the other hand, if you have access to a continuous power source and can keep your camera plugged in, [auto] is the way to go. It’s always good to keep your camera online, it can make things a lot easier and save you from any potential connectivity issues. Plus, you'll be able to access your camera conveniently whenever your phone is nearby. However, keeping it online is quite power consuming if being honest.
In conclusion, if the battery is fully charged and the Power Saving is set to [Auto], then I think the camera can easily survive the standby mode and complete the recording without any issues.