In my understanding you want to process user input data by data_verify so it would be more efficient and less misleading to redesign and rename sub data_verify e.g. to process_input and call after each <>

sub process_input{
    my $data = shift;
    chomp($data);      # cut off newline
    $data =~ s/^\s*//; # remove leading blanks
    $data =~ s/\s*$//; # remove trainilg blanks
    return $data; 
}
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I would store the given information in a hash rather than an array, but that's my personal preference.

if ( ( $option !~ m{/^\d$/}xms ) or ( $option <= 0 ) or ( $option > 10 ) ) {
should be better /^\d+$/ otherwise it will match only single digits and you will never be able to quit (10).

seperate main_menu from db_connect to an extra sub would be better understandable

... I'm just thinking loudly ... oh, did I write that ?