SELECT 
  f.feature_id, 
  f.purpose, 
  p.product_id, 
  p.parent_product_id, 
  g.id, 
  g.code 
FROM 
  cscart_product_variation_group_features AS f 
  INNER JOIN cscart_product_variation_groups AS g ON f.group_id = g.id 
  INNER JOIN cscart_product_variation_group_products AS p ON f.group_id = p.group_id 
WHERE 
  p.product_id IN (125, 120, 117, 113, 68)

Query time 0.00066

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "g",
          "access_type": "ALL",
          "possible_keys": ["PRIMARY"],
          "rows": 2,
          "filtered": 100
        }
      },
      {
        "block-nl-join": {
          "table": {
            "table_name": "f",
            "access_type": "ALL",
            "possible_keys": ["idx_group_id"],
            "rows": 3,
            "filtered": 100
          },
          "buffer_type": "flat",
          "buffer_size": "4Kb",
          "join_type": "BNL",
          "attached_condition": "f.group_id = g.`id`"
        }
      },
      {
        "block-nl-join": {
          "table": {
            "table_name": "p",
            "access_type": "ALL",
            "possible_keys": ["PRIMARY", "idx_group_id"],
            "rows": 9,
            "filtered": 55.55555725,
            "attached_condition": "p.product_id in (125,120,117,113,68)"
          },
          "buffer_type": "incremental",
          "buffer_size": "1Kb",
          "join_type": "BNL",
          "attached_condition": "p.group_id = g.`id`"
        }
      }
    ]
  }
}