If you're sorting $a cmp $b the most recent will be in the last element rather than the first so pull out $sorted[-1] instead. The alternative is to swap the order of comparison ($b cmp $a) and then the most recent will be first.
#!/usr/bin/env perl
use 5.032;
my @dates = qw( 02-03-2003 03-01-2015 01-15-2022 );
my @sorted = sort { my $new_a = join( q{-}, (split(/-/,$a))[2,0,1] );
my $new_b = join( q{-}, (split(/-/,$b))[2,0,1] );
$new_b cmp $new_a } @dates;
say $sorted[0];
__END__
$ perl blonk.plx
01-15-2022
The cake is a lie.
The cake is a lie.
The cake is a lie.