Nothing is actually wrong with your code. Enter numbers one per line.

$type 1226028.pl
use feature qw(say state);
say "Please input numbers to be summed. Crtl-D to stop";
my $user_total = &total(<STDIN>);
chomp($user_total);

print "The total of inputted numbers is $user_total \n";

sub total {
    state $sum = 0;
    state $number;

    foreach my $number (@_) {
        $sum += $number;
    }

    return $sum;

}

$perl 1226028.pl
Please input numbers to be summed. Crtl-D to stop
12
12
^Z
The total of inputted numbers is 24
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Note: I added 'feature' statement and used CTRL-Z rather than CTRL-D