Some thoughts

my @xml_files = glob( '*xml' );
#say for @xml_files;

my @bak_files = glob( '*bak' );
#say for @bak_files;

dddie("impossible, uneven number of files ", \@xml_files, \@bak_files 
+) if @xml_files != @bak_files;

my %seen;
for my $orig ( @xml_files ) {
    my $bak = "$orig.bak";
    $seen{ $orig } ++;
    $seen{ $bak } ++;
    
}

for my $bak ( @bak_files ){
    my $orig =  $bak;
    $orig =~ s/\.bak$//;
    die "IMPOSSIBLE" if not exists $seen{ $orig } and not exists $seen
+{ $bak };
}
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</c>