Prompted to enter new password for Gmail on Android for no apparent reason
I have all but confirmed through toggling my cell phone from Wi-Fi to 4G that the long address is indeed the network IP address (Verizon service) that my phone used to access my Gmail address when I was in transit (outside the Wi-Fi boundaries).
Although this is a partial reply to the question, and in truth I still can't figure out why I was prompted to enter a different password, there has been zero strange activity that I could detect, or that Google recorded on any tracking or notification system.
So what did I learn:

Cell tower IP addresses may not match the State you are connecting from under the Last account activity at the bottom of the Inbox on the Gmail display on a laptop.
Confirm this by going to Settings on Android, selecting System, About phone, Network, and watching the IP address change as the phone is switched from Wi-Fi to 4G.
On Android, go to Manage your Google Account under Settings, then Security, and check Recent security activity to make sure any password changes were legit, and there were no new devices signed in. Also check Your devices under the same tab to make sure all devices are recognized.
If not your phone (for 2-step verification) it is at least worthwhile to link the account to some other Google account, since the absence of notifications as to any attempt at logging onto the account by an unrecognized device is reassuring.