This tweak adds a newline to the first heading in a series:

while ( defined (my $line = <DATA> ) )
{
   state $indent_char = '';
   print "\n" if $line =~ m/$opening_pattern/ && ! $indent_char;
   $indent_char = '' if $line =~ m/$closing_pattern/;
   print $indent_char . $line;
   $indent_char = '  ' if $line =~ m/$opening_pattern/;
}
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