How to correctly augment Any?

First of all: augmenting core classes, at least in the foreseeable future of Rakudo Perl 6, is not a good idea. It doesn't play well with precompilation.

Secondly: when a class is a subclass of another class, the subclass "knows" from which it inherits. Alas, this doesn't work the other way around: a class does not know of its subclasses (at least at the moment of this writing).

This means that if you augment Any, none of its subclasses know that should also re-compose themselves. In your first example, you do that with the List class by augmenting that. However, if you would reverse the order of the augments, it wouldn't work either, because the List class would get re-composed before the Any class would get re-composed.

It's therefore that it's recommended to mix any extra methods using roles, either into a class, or into an object (mixins of roles)

A summary of the various comments here and on the issue I created on Github:

As Liz mentioned currently the children types do not see augmentations of their parents. This is true unless there was a flush of the method cache for that type.

This behaviour is a known limitation that will be fixed some time in the future with low priority.

Reconstructing the class with .^compose can be used to make augmented methods known to the children:

use v6.c;

use MONKEY-TYPING;

augment class Any {
    method show0 { self.say }}

List.^compose;

<hello world>.show0; # OUTPUT: (hello world)

Alternatively the qualified class can be accessed directly:

use v6.c;

use MONKEY-TYPING;

augment class Any {
    method show0 { self.say }}

<hello world>.Any::show0; # OUTPUT: (hello world)