SELECT 
  cscart_product_prices.product_id, 
  MIN(
    IF(
      cscart_product_prices.percentage_discount = 0, 
      cscart_product_prices.price, 
      cscart_product_prices.price - (
        cscart_product_prices.price * cscart_product_prices.percentage_discount
      )/ 100
    )
  ) AS price 
FROM 
  cscart_product_prices 
WHERE 
  cscart_product_prices.product_id IN (
    5822, 5823, 12916, 12921, 12956, 12958, 
    13014, 13028, 13040, 13052, 12960, 
    12974
  ) 
  AND cscart_product_prices.lower_limit = 1 
  AND cscart_product_prices.usergroup_id IN (0, 1) 
GROUP BY 
  cscart_product_prices.product_id

Query time 0.00054

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "8.41"
    },
    "grouping_operation": {
      "using_filesort": false,
      "table": {
        "table_name": "cscart_product_prices",
        "access_type": "range",
        "possible_keys": [
          "usergroup",
          "product_id",
          "lower_limit",
          "usergroup_id"
        ],
        "key": "product_id",
        "used_key_parts": [
          "product_id"
        ],
        "key_length": "3",
        "rows_examined_per_scan": 12,
        "rows_produced_per_join": 2,
        "filtered": "20.00",
        "index_condition": "(`gaseus`.`cscart_product_prices`.`product_id` in (5822,5823,12916,12921,12956,12958,13014,13028,13040,13052,12960,12974))",
        "cost_info": {
          "read_cost": "8.17",
          "eval_cost": "0.24",
          "prefix_cost": "8.41",
          "data_read_per_join": "57"
        },
        "used_columns": [
          "product_id",
          "price",
          "percentage_discount",
          "lower_limit",
          "usergroup_id"
        ],
        "attached_condition": "((`gaseus`.`cscart_product_prices`.`lower_limit` = 1) and (`gaseus`.`cscart_product_prices`.`usergroup_id` in (0,1)))"
      }
    }
  }
}

Result

product_id price
5822 0.00000000
5823 0.00000000
12916 466.00000000
12921 720.00000000
12956 1610.00000000
12958 2380.00000000
12960 639.00000000
12974 987.00000000
13014 1200.00000000
13028 1430.00000000
13040 1540.00000000
13052 1680.00000000