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<?php
namespace Namespace\Mymodule\Observer;
 
use Magento\Framework\Event\ObserverInterface;
use Magento\Framework\App\RequestInterface;
 
class SetAdditionalOptions implements ObserverInterface
{
    /**
     * @var RequestInterface
     */
    protected $_request;
     
    /**
     * @param RequestInterface $request
     */
    public function __construct(
        RequestInterface $request
    ) {
        $this->_request = $request;
    }
 
    /**
     * @param \Magento\Framework\Event\Observer $observer
     */
    public function execute(\Magento\Framework\Event\Observer $observer)
    {
        // Check and set information according to your need
        if ($this->_request->getFullActionName() == 'checkout_cart_add') { //checking when product is adding to cart
            $product = $observer->getProduct();
            $additionalOptions = [];
            $additionalOptions[] = array(
                'label' => "Some Label",
                'value' => "Your Information",
            );
            $observer->getProduct()->addCustomOption('additional_options', serialize($additionalOptions));
        }
    }
}

<?php
namespace Namespace\Mymodule\Observer;
 
use Magento\Framework\Event\ObserverInterface;
use Magento\Framework\App\RequestInterface;
use Magento\Framework\Serialize\SerializerInterface;
 
class SetAdditionalOptions implements ObserverInterface
{
    /**
     * @var RequestInterface
     */
    protected $_request;
     
    /**
     * @param RequestInterface $request
     */
    public function __construct(
        RequestInterface $request,
        SerializerInterface $serializer
    ) {
        $this->_request = $request;
        $this->serializer = $serializer;
    }
 
    /**
     * @param \Magento\Framework\Event\Observer $observer
     */
    public function execute(\Magento\Framework\Event\Observer $observer)
    {
        // Check and set information according to your need
        if ($this->_request->getFullActionName() == 'checkout_cart_add') { //checking when product is adding to cart
            $product = $observer->getProduct();
            $additionalOptions = [];
            $additionalOptions[] = array(
                'label' => 'Some Label',
                'value' => 'Some Info',
            );
            $observer->getProduct()->addCustomOption('additional_options', $this->serializer->serialize($additionalOptions));
        }
    }
}

https://www.codedecorator.com/blog/how-to-additional-options-in-cart-item-magento2/ (Magento2.4)

Step 1. Create registration.php and module.xml file for custom module.

step 2. Assign Observers to Events

path - /app/code/Namespace/Mymodule/etc/events.xml

step 3. Create the Observers path - app/code/Namespace/Mymodule/Observer/SetAdditionalOptions.php

    <?php
 
namespace Namespace\Mymodule\Observer;
 
use Magento\Framework\Event\ObserverInterface;
use Magento\Framework\App\RequestInterface;
 
class SetAdditionalOptions implements ObserverInterface
{
    /**
     * @var RequestInterface
     */
    protected $_request;
     
    /**
     * @param RequestInterface $request
     */
    public function __construct(
        RequestInterface $request
    ) {
        $this->_request = $request;
    }
 
    /**
     * @param \Magento\Framework\Event\Observer $observer
     */
    public function execute(\Magento\Framework\Event\Observer $observer)
    {
        // Check and set information according to your need
        if ($this->_request->getFullActionName() == 'checkout_cart_add') { //checking when product is adding to cart
            $product = $observer->getProduct();
            $additionalOptions = [];
            $additionalOptions[] = array(
                'label' => "Some Label",
                'value' => "Your Information",
            );
            $observer->getProduct()->addCustomOption('additional_options', serialize($additionalOptions));
        }
    }
}

rm -rf var/di var/generation var/cache/* var/log/* var/page_cache/*

php bin/magento setup:upgrade

php bin/magento setup:di:compile

php bin/magento cache:clean

php bin/magento cache:flush

php bin/magento indexer:reindex

Step 1: Create registration.php and module.xml file the for custom module.

Step 2: Assign Observers to Events

/app/code/Namespace/Mymodule/etc/events.xml

Step 3: Create the Observers

app/code/Namespace/Mymodule/Observer/SetAdditionalOptions.php

<?php
namespace Namespace\Mymodule\Observer;
 
use Magento\Framework\Event\ObserverInterface;
use Magento\Framework\App\RequestInterface;
 
class SetAdditionalOptions implements ObserverInterface
{
    /**
     * @var RequestInterface
     */
    protected $_request;
     
    /**
     * @param RequestInterface $request
     */
    public function __construct(
        RequestInterface $request
    ) {
        $this->_request = $request;
    }
 
    /**
     * @param \Magento\Framework\Event\Observer $observer
     */
    public function execute(\Magento\Framework\Event\Observer $observer)
    {
        // Check and set information according to your need
        if ($this->_request->getFullActionName() == 'checkout_cart_add') { //checking when product is adding to cart
            $product = $observer->getProduct();
            $additionalOptions = [];
            $additionalOptions[] = array(
                'label' => "Some Label",
                'value' => "Your Information",
            );
            $observer->getProduct()->addCustomOption('additional_options', serialize($additionalOptions));
        }
    }
}

run below command after

rm -rf var/di var/generation var/cache/* var/log/* var/page_cache/*

php bin/magento setup:upgrade

php bin/magento setup:di:compile

php bin/magento cache:clean

php bin/magento cache:flush

php bin/magento indexer:reindex