If you want to use subroutines (as you should) then try passing parameters into your subroutines. The following code works for me. (Read: It does not produce any warnings or errors and the Excel file is properly formatted).

#!/bin/env perl
use strict;
use warnings;
use Excel::Writer::XLSX;

my $workbook = Excel::Writer::XLSX->new( 'mytest.xlsx' );
my $worksheet = $workbook->add_worksheet( 'testsheet' );

write_me( $workbook, $worksheet );

sub write_me
{
    my ( $workbook, $worksheet ) = @_;

    my $text_format = $workbook->add_format(
        bold   => 1,
        italic => 1,
        color  => 'red',
        size   => 18,
        font   => 'Lucida Calligraphy'
    );

    my $result = $worksheet->write( 'A2', "Text" );
    print "my result = $result\n";

    $worksheet->write( 'B3', "Hello Excel", $text_format );
}
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