Sounds like the dates are in the yyyy/mm/dd format, so why not just compare the strings with lt/gt?

sub validate_date {
   my ($start_date, $end_date, $today) = @_;
   return "Invalid format for start date (expecting yyyy/mm/dd)"
      if $start_date !~ m{^\d{4}/\d{2}/\d{2}\z};
   return "Invalid format for end date (expecting yyyy/mm/dd)"
      if $end_date !~ m{^\d{4}/\d{2}/\d{2}\z};
   return "End date must be no later than today"
      if $end_date gt $today;
   return "Start date must be no later than end date"
      if $start_date gt $end_date;
   return "";
}
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