You don't need $user as part of your key, since $session_id is unique. If you want to retrieve something, store it in the value part of the hash. The key is for stuff you want to look up by. So:

$session_hash{$session_id} = [$dept_code, $user]; #array ref
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and in write_id, the magical print will be

print DATA join(',', @$output), "\n";
# Or something like that
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Review perldoc perlreftut to get a better handle on how complex data structures are built in Perl.