I'm trying to get this PHP array to correctly display the html with embedded variables. However, it just displays the variables, and php within the html, as plain text (the href works, but it link you to '', instead of the value of the PHP variable).
$total_rows['cart_sold_by'] = array(
'label' => __( 'Sold by:', 'woocommerce' ),
'value' => '<a href="<?php echo $user_LINK; ?>"><?php echo $user_NAME; ?></a>'
);
Do the following changes in your code and check it again.
$total_rows['cart_sold_by'] = array( 'label' => __( 'Sold by:', 'woocommerce' ), 'value' => '<a href="'.$user_LINK.'">'.$user_NAME.'</a>' );
you are using php tags inside of a php tag, simply just concat the strings. Do something like
'value' => '<a href=" ' .$user_LINK.' ">'. $user_NAME . '</a>'