Adding Custom Endpoint in WordPress Rest API

Instead ID you should use cat_ID

$data[$i]['id'] = $category->cat_ID;

get_categories() return list of category objects with:

"term_id": 7,
"name": "default",
"slug": "default",
"term_group": 0,
"term_taxonomy_id": 7,
"taxonomy": "category",
"description": "",
"parent": 0,
"count": 11,
"filter": "raw",
"cat_ID": 7,
"category_count": 11,
"category_description": "",
"cat_name": "Analiza",
"category_nicename": "default",
"category_parent": 0