...that whenever $WorkingCopy{$key}= /p1/ was true (i.e., matched the value), "this" would be assigned to $WorkingCopy{$key}; if false (match failed) "that" would be assigned to $WorkingCopy{$key}

Perhaps you meant

  $WorkingCopy{$key} = $WorkingCopy{$key} =~ /p1/ ? "this" : "that";
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(as you have it, /p1/ is being matched against $_)