Show category in post page, that is in specific category

You should use get_the_category() instead of get_categories().

The get_the_category() function will return only categories assigned to the post, while get_categories() that you use returns all existing categories.

Edit:

To get categories assigned to post, but only those with the ancestor Food, you can use code:

$args = [
    'object_ids' => get_the_ID(),   // only categories assigned to current post
    'child_of' => {ID_of_food_cat}  // limit results to children (descendants) of this category
];
$cats = get_categories($args);

ID of parent category can be hard-coded or dynamic:

$food_cat_id = get_category_by_slug('food');  // <-- slug of Food
$food_cat_id = ($food_cat_id instanceof WP_Term) ? $food_cat_id->term_id : 0;