Adding RaiseError => 1 to the connect call might also work for you in which case you won't have to add || die ... after each call.

You also have the ability to change the behavior of die by installing a custom $SIG{__DIE__} handler:

$SIG{__DIE__} = sub {
  print STDERR @_;
  print STDOUT ...; # whatever you want
  exit(1);
};
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Just throwing some out some ideas/options.

Update: if RC-E represents some sort of context or scope that you want to report via STDOUT, you could use a localize global variable to remember what the current context is.

our $::error_context;
{
  local $::error_context = "RC-E";
  $dbh->prepare(...); # dbh call in the RC-E context
  {
    local $::error_context = "RC-F";
    $dbh->whatever(...); # dbh call in the RC-F context
  }
  # back to context "RC-E"
  ...
}
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Then the SIG{__DIE__} handler can determine the context by inspecting $::error_context.