An async method cannot return any type that has an accessible GetAwaiter method

It says here:

Async methods can have the following return types:

Task, for an async method that performs an operation but returns no
value.

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Task, for an async method that returns a value.

void, for an event handler.

Starting with C# 7.0, any type that has an accessible GetAwaiter
method. The object returned by the GetAwaiter method must implement
the System.Runtime.CompilerServices.ICriticalNotifyCompletion
interface.

Starting with C# 8.0, IAsyncEnumerable, for an async method that
returns an async stream.

Question. How to understand the phrase: Asynchronous methods can have the following return types…any type that has an accessible GetAwaiter method, if the actual is not?

This code is not working:

using System.Runtime.CompilerServices;

async A Method() //Error CS1983 The return type of an async method must be void, Task, Task<T>, a task-like type, IAsyncEnumerable<T>, or IAsyncEnumerator<T>
{
    await new A();
}

class A
{
    public TaskAwaiter GetAwaiter()
    {
        return new TaskAwaiter();
    }
}

>Solution :

The summary docs are a bit confusing. GetAwaiter is insufficient to be used as a return type; GetAwaiter is more about await than async.

The more detailed docs clarify:

In addition, the type returned from the GetAwaiter method must have the System.Runtime.CompilerServices.AsyncMethodBuilderAttribute attribute.

The AsyncMethodBuilder attribute gives the compiler sufficient information to actually build and control the return type instance from the async state machine.

TaskAwaiter<T> does not have this attribute. It doesn’t normally need it because task return types are "grandfathered in" and treated specially by the compiler.