I’d use a GRT variant.

use List::Util qw( max );

my @padded = do {
    my @copy = @path;
    my @segment_length;
    while( 1 ) {
        my $len = max map { s!([^/]*/|[^/]+)!! ? length( $1 ) : -1 } @
+copy;
        last if $len == -1;
        push @segment_length, $len;
    }
    my $format = join '', map "%${_}s", @segment_length;
    map {;
        no warnings 'uninitialized';
        sprintf $format, split m!/!, $_, -1;
    } @path;
};

@path = @path[ sort { $padded[ $a ] cmp $padded[ $b ] } 0 .. $#padded 
+];
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Makeshifts last the longest.