Get the product category terms from cart items in WooCommerce

First your $product_cat variable is not defined.

To get a product category on cart items, you need to get the parent variable product ID for product variations as they don't handle custom taxonomies as product categories or product tags.

To get the correct product ID for any custom taxonomy terms on cart items always use:

$product_id = $cart_item['product_id']; 

Instead of:

$product_id = $cart_item['data']->get_id(); 

Now if you need to get the product category term names, instead of using get_the_terms() function, you can use wp_get_post_terms() and implode() functions like:

$term_names = wp_get_post_terms( $product_id, 'product_cat', ['fields' => 'names'] );

// Displaying term names in a coma separated string
if( count( $term_names ) > 0 )
    echo __("Product categories") . ": " . implode( ", ", $term_names ) . '<br>':

// OR displaying term names as a vertical list
if( count( $term_names ) > 0 )
    echo __("Product categories") . ": " . implode( "<br>", $term_names ) . '<br>';

So in a cart items foreach loop:

// Loop through cart items
foreach ( WC()->cart->get_cart() as $cart_item_key => $cart_item ) {
    $quantity     = $cart_item['quantity']; 
    $product_id   = $cart_item['product_id'];
    $variation_id = $cart_item['variation_id'];

    echo __("PRODUCT ID: ") . $product_id . "<br>";

    $term_names = wp_get_post_terms( $product_id, 'product_cat', array('fields' => 'names') );

    if ( count($term_names) > 0 ) {
        echo __("PRODUCT CATEGORY: ") . implode("<br>", $term_names) . "<br>";
    }
}