The fact that you are not getting success/failure emails when trying to upgrade validates that your cron is NOT working - unless you have the wrong email address setup. The screenshot you attached it really small but it looks like you have this part in the actual command line:

SHELL="/usr/bin/bash" *    *    *    *    *

You shouldn't need that in the command. All you should need is this part (your may vary)

 /opt/plesk/php/7.1/bin/php -q /var/www/vhosts/mywebsite.com/httpdocs/periodic/cron.php 

So try removing the SHELL="/usr/bin/bash" *    *    *    *    *  part in the command box and see if that will work.