Re: /storage/emulated/0/
Despite the name, on modern Android version this is the "large built-in memory" NOT the real microSd.
Re: Does AM use the Android Backup Service to backup its settings to Google Drive?
Android Backup Service and Google Drive are two separate unrelated things (at least what they "look like" to an app or a user).
And no, Aqua Mail does not use the Android Backup Service because the Google developer agreement for this service specifically prohibits storing user's account IDs or passwords.
Re: A backup does you no good if you can't restore from it, or from the path on which it lives.
And why is this?
The "large built-in storage" is perfectly accessible (readable and writable), is the default, no issues at all.
If you think you're going to reset you phone (including formatting this storage) - why not either make a copy of this file in a safe location and/or use Aqua Mail's built-in "upload backup to / download from" Google Drive / OneDrive / Box.com / Dropbox?
And btw, microSd cards sometimes go dead so that's not bulletproof either