In my point of view, if you start the project, you can use something similar to following very simplified module:

package MyProject::Database;

use DBI;

our $dbh;

sub getDbh {
  #you should catch the exceptions and try to reconnect here
  if ($dbh) {
    $dbh->ping();
  } else {
    $dbh = DBI->connect();
  }
  return $dbh;
}

sub doSQL {
  my $dbh = getDbh();
  return $dbh->do(@_);
}

sub query2aref {
  my $dbh = getDbh();
  return $dbh->selectall_arrayref(@_);
}

1;
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Of course, for some reasons it is better to implement it as object instance, there is many ways how to do it...