You test whether a file exists using -e. Together with some cleanup, that means:

use Fcntl 'O_RDWR';

for my $id ( @row ) {
    my $fname = "../XML/$id.xml";
    
    next if not -e $fname;

    tie my @array, 'Tie::File', $fname, mode => O_RDWR; 
    splice @array, 2, 0, "<database_id=\"gl:redunant\">";
    untie @array;
}
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Makeshifts last the longest.