You didn’t specify, but I’m presuming you logged back into your iCloud account; assuming you have Keychain enabled, this is why it knew your network.
I’m still wishing you’d tried a battery drain with benign videos, rather than a GPS app that complicates what radios and background processes are involved, but ultimately it shouldn’t matter if that app didn’t have a bug that was at the root of the original problem.
I think that’s related in part to WiFi calling and 911 location services, assuming you have enabled WiFi calling and calls on other devices. It may also just be a system service that, if given permissions, an app can use to help tag your location for legitimate reasons (Uber, etc).
That’s usually difficult to do, as the ipad wants to restart automatically when connected to a charger, but I don’t think it matters in this case.
I’m not entirely clear if you believe you have some perceived improvement with a factory reset or not; if not, it’s time for a trip to battery town, or to ifixt if you’re game to do it yourself. I find it to be a reasonably easy model to swap batteries; it’s screen repair due to the laminate that is far too challenging for the average person.
Curious as to your decision, or if you have further questions.