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 = 310 
WHERE 
  cscart_products_categories.product_id IN (
    348, 351, 370, 820, 794, 795, 2754, 2803, 
    2874, 2799, 1406, 796, 797, 798, 2656, 
    800, 799, 2667, 804, 801
  ) 
GROUP BY 
  cscart_products_categories.product_id

Query time 0.00129

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "29.16"
    },
    "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": 21,
            "rows_produced_per_join": 21,
            "filtered": "100.00",
            "index_condition": "(`zdrowy_db`.`cscart_products_categories`.`product_id` in (348,351,370,820,794,795,2754,2803,2874,2799,1406,796,797,798,2656,800,799,2667,804,801))",
            "cost_info": {
              "read_cost": "12.36",
              "eval_cost": "2.10",
              "prefix_cost": "14.46",
              "data_read_per_join": "336"
            },
            "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": 21,
            "filtered": "100.00",
            "cost_info": {
              "read_cost": "5.25",
              "eval_cost": "2.10",
              "prefix_cost": "21.81",
              "data_read_per_join": "336"
            },
            "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": 1,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "5.25",
              "eval_cost": "0.11",
              "prefix_cost": "29.16",
              "data_read_per_join": "6K"
            },
            "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
348 310M 32
351 310M 33
370 310M 34
794 310M 10
795 310M 12
796 310M 15
797 310M 16
798 310M 17
799 310M 18
800 310M 19
801 310M 20
804 310M 21
820 310M 31
1406 310M 13
2656 310M 0
2667 310M 0
2754 310M 0
2799 310M 0
2803 310M 0
2874 310M 0