Try below code and i have tested my code it's working.
public function execute(Observer $observer){
$writer = new \Zend_Log_Writer_Stream(BP . '/var/log/categoriesIds.log');
$logger = new \Zend_Log();
$logger->addWriter($writer);
$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$quote = $observer->getEvent()->getQuote();
$cartItemsList = $quote->getAllItems();
foreach ($cartItemsList as $item) {
$productId = $item->getProductId();
$product = $objectManager->create('Magento\Catalog\Model\Product')->load($productId);
$categoriesIds = $product->getCategoryIds();
$logger->info(print_r($categoriesIds, true));
}
}
See my output.

If any query let me know.
THANKS.