尝试修改

public function update_product($product_id, $data, $method = "PUT") {

    return $this->_make_api_call('products/' . $product_id, $data, $method);
}

仅将$ data作为第二个参数传递给update_product

Pass only $data as 2nd parameter to update_product

$data=  json_encode(

    array( 'product' =>

       array( 
          'regular_price'        => "10.26",
          'managing_stock'   => true,
          'in_stock'         => true,
          'stock_quantity'   => 45
       )
    )
);