The DBI *_hashref methods are the slowest way to fetch. Here's a shorter and faster version for you. (The columns you named are returned 6th and 8th {0-indexed}, respectively)

sub sizeOfDB {
   my $db = shift;
   my $size = 0;
   
   # No placeholders needed, so let selectall_* do the annoying stuff
   my $result = $db->selectall_arrayref('show table status');

   # Assume that the call succeeded, either check error or use {RaiseE
+rror=>1}
   foreach (@$result) { $size += $_->[6] + $_->[8] }

   return $size;
}
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