All-core MediaWiki website upgrade script
Naming
Try not to use generic names like $file. Make your code read easy for others. Say $files_to_backup for example.

Check for errors when it matters
If backup is important: check that the backups succeeded:

if cp "${files[@]}"${war}/mediawiki_specific_backups";then
     rm -rf "${war}/${domain}"
     mkdir "${war}/${domain}"
     ...
     ...
 else
    # handle error condition
fi


Document the code
I prefer a comment in the script header describing what the script. If the script does useful work, document what it does so others understand what it does and how to use it. Similarly, comment anything in the code which is important and you think might require some explanation to help readers.

#!/bin/sh
# Usage: how-to-use-script
# Purpose: upgrade all core MediaWiki websites
# etc