Presently there is no equivalent to @Order when using functional bean registration to allow ordering of beans outside of the bean implementation (where @Order, Ordered, PriorityOrdered etc can be used):

    // no attribute for order, no access to BeanDefinition, and BeanDefinition doesn't have an order attribute
    bean<SomeBean>(name = "abc", ...) 
    @Bean
    @Order(33)  // bean ordering set separately from bean implementation
    fun someBean() = SomeBean()

@Order works at sort time (provider.orderedStream() or injecting a List<> of beans) by introspecting the factory method looking for @Order via an implementation of OrderComparator.OrderSourceProvider that uses beanDefinition.getResolvedFactoryMethod() (org.springframework.beans.factory.support.DefaultListableBeanFactory.FactoryAwareOrderSourceProvider).

It would be useful to have order as an optional first-class property on BeanDefinition which would allow the functional bean registration API to (optionally) provide an order and furthermore allow @Order processing to be collapsed to the same mechanism, while also providing future capabilities for any bean registration capability to support bean ordering.

Without this capability there is no mechanism for functional bean registration to provide bean ordering external to the bean implementation, as is possible with @Order.