What is this "com.android.backupconfirm"? What is the package on my phone that is called com.android.backupconfirm? I tried Googling and found an answer on a random forum that said that is the UI for the backup confirmation dialog. While this sounds correct, could you explain why this isn't a part of the core but instead a separate package?
After googling around a little, I found the source code of BackupRestoreConfirmation.java, which is used to build the package com.android.backupconfirm. Quoting from its comments:


  Confirm with the user that a requested full backup/restore operation is legitimate.
  Any attempt to perform a full backup/restore will launch this UI and wait for a designated timeout interval (nominally 30 seconds) for the user to confirm.  If the user fails to respond within the timeout period, or explicitly refuses the operation within the UI presented here, no data will be transferred off the device.


So this confirms what I already guessed in my comment on the question itself: it's belonging to the dialog popping up when initiating adb backup, and which does nothing but asking you to confirm whether the remotely triggered backup should be executed (and if you want to protect it with a password).

As the comment is further speaking of a backup manager service, one could also think of the Google Cloud Backup (see: google-backup). So let me again stress some important keywords from the comment's start:


  a requested full backup/restore operation


Google Cloud backup neither is a "full backup/restore operation", nor can it be "requested" by the user. The only backup service this applies to is adb backup.