SELECT 
  cscart_products_categories.product_id, 
  GROUP_CONCAT(
    IF(
      cscart_products_categories.link_type = "M", 
      CONCAT(
        cscart_products_categories.category_id, 
        "M"
      ), 
      cscart_products_categories.category_id
    )
  ) AS category_ids, 
  product_position_source.position AS position 
FROM 
  cscart_products_categories 
  INNER JOIN cscart_categories ON cscart_categories.category_id = cscart_products_categories.category_id 
  AND cscart_categories.storefront_id IN (0, 1) 
  AND (
    cscart_categories.usergroup_ids = '' 
    OR FIND_IN_SET(
      0, cscart_categories.usergroup_ids
    ) 
    OR FIND_IN_SET(
      1, cscart_categories.usergroup_ids
    )
  ) 
  AND cscart_categories.status IN ('A', 'H') 
  LEFT JOIN cscart_products_categories AS product_position_source ON cscart_products_categories.product_id = product_position_source.product_id 
  AND product_position_source.category_id = 290 
WHERE 
  cscart_products_categories.product_id IN (
    1139, 1164, 1165, 640, 1168, 1159, 1163, 
    2541, 1711, 2679, 2835, 2836, 2837, 
    1213, 1225
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00125

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "23.31"
    },
    "grouping_operation": {
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "cscart_products_categories",
            "access_type": "range",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "pt",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "rows_examined_per_scan": 17,
            "rows_produced_per_join": 17,
            "filtered": "100.00",
            "index_condition": "(`zdrowy_db`.`cscart_products_categories`.`product_id` in (1139,1164,1165,640,1168,1159,1163,2541,1711,2679,2835,2836,2837,1213,1225))",
            "cost_info": {
              "read_cost": "9.71",
              "eval_cost": "1.70",
              "prefix_cost": "11.41",
              "data_read_per_join": "272"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        },
        {
          "table": {
            "table_name": "product_position_source",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id",
              "product_id"
            ],
            "key_length": "6",
            "ref": [
              "const",
              "zdrowy_db.cscart_products_categories.product_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 17,
            "filtered": "100.00",
            "cost_info": {
              "read_cost": "4.25",
              "eval_cost": "1.70",
              "prefix_cost": "17.36",
              "data_read_per_join": "272"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "position"
            ]
          }
        },
        {
          "table": {
            "table_name": "cscart_categories",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id"
            ],
            "key_length": "3",
            "ref": [
              "zdrowy_db.cscart_products_categories.category_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "4.25",
              "eval_cost": "0.09",
              "prefix_cost": "23.31",
              "data_read_per_join": "5K"
            },
            "used_columns": [
              "category_id",
              "usergroup_ids",
              "status",
              "storefront_id"
            ],
            "attached_condition": "((`zdrowy_db`.`cscart_categories`.`storefront_id` in (0,1)) and ((`zdrowy_db`.`cscart_categories`.`usergroup_ids` = '') or (0 <> find_in_set(0,`zdrowy_db`.`cscart_categories`.`usergroup_ids`)) or (0 <> find_in_set(1,`zdrowy_db`.`cscart_categories`.`usergroup_ids`))) and (`zdrowy_db`.`cscart_categories`.`status` in ('A','H')))"
          }
        }
      ]
    }
  }
}

Result

product_id category_ids position
640 293,585M
1139 292M
1159 293,585M
1163 585M
1164 292M
1165 292M
1168 293,585M
1213 292M
1225 292M
1711 291M
2541 585M
2679 291M
2835 292M
2836 292M
2837 292M