The example from the Net::IMAP::Simple docs works fine to get the message id if you ask for the Message-ID header attribute:

use Net::IMAP::Simple;
use Email::Simple;

my $server = Net::IMAP::Simple->new( 'someserver' );
$server->login( 'someuser', 'somepassword' );
    
my $nmessages = $server->select( 'somefolder' );

foreach my $msg ( 1 .. $number_of_messages ) {
    print "This message has been read before...\n"
      if $server->seen( $msg );

    my $email = Email::Simple->new( join '', @{$server->get( $msg )} )
+;
        
    print $email->header('Message-ID'), "\n";
}

$server->quit();
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