Why is my OpenCart page full of "Notice: Undefined index" warnings?

Notice: Undefined index (and on PHP 8, Warning: Undefined array key) appears when a template or controller reads an array key that wasn’t set, usually after a PHP version bump or a theme/extension that wasn’t written for your version. They flood the header, product and category pages. We harden the controller data and templates so the keys are always defined, then quiet the log, without masking genuine errors.