feat(aws-eks): support bottlerocket managed nodegroup (#17323)

Support Bottlerocket managed nodegroups and update the README as Bottlerocket has been supported in all AWS commercial regions since its [GA](https://aws.amazon.com/tw/about-aws/whats-new/2020/08/announcing-general-availability-of-bottlerocket/).

Fixes: #17324

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

packages/@aws-cdk/aws-eks/README.md

@@ -458,9 +458,16 @@ To disable the installation of the termination handler, set the `spotInterruptHa
 #### Bottlerocket
 
 [Bottlerocket](https://aws.amazon.com/bottlerocket/) is a Linux-based open-source operating system that is purpose-built by Amazon Web Services for running containers on virtual machines or bare metal hosts.
-At this moment, `Bottlerocket` is only supported when using self-managed auto-scaling groups.
 
-> **NOTICE**: Bottlerocket is only available in [some supported AWS regions](https://github.com/bottlerocket-os/bottlerocket/blob/develop/QUICKSTART-EKS.md#finding-an-ami).
+`Bottlerocket` is supported when using managed nodegroups or self-managed auto-scaling groups.
+
+To create a Bottlerocket managed nodegroup:
+
+```ts
+cluster.addNodegroupCapacity('BottlerocketNG', {
+  amiType: NodegroupAmiType.BOTTLEROCKET_X86_64,
+});
+```
 
 The following example will create an auto-scaling group of 2 `t3.small` Linux instances running with the `Bottlerocket` AMI.
 
@@ -480,6 +487,8 @@ For example, if the Amazon EKS cluster version is `1.17`, the Bottlerocket AMI v
 
 Please note Bottlerocket does not allow to customize bootstrap options and `bootstrapOptions` properties is not supported when you create the `Bottlerocket` capacity.
 
+For more details about Bottlerocket, see [Bottlerocket FAQs](https://aws.amazon.com/bottlerocket/faqs/) and [Bottlerocket Open Source Blog](https://aws.amazon.com/blogs/opensource/announcing-the-general-availability-of-bottlerocket-an-open-source-linux-distribution-purpose-built-to-run-containers/).
+
 ### Endpoint Access
 
 When you create a new cluster, Amazon EKS creates an endpoint for the managed Kubernetes API server that you use to communicate with your cluster (using Kubernetes management tools such as `kubectl`)

packages/@aws-cdk/aws-eks/lib/managed-nodegroup.ts

@@ -34,7 +34,15 @@ export enum NodegroupAmiType {
   /**
    * Amazon Linux 2 (ARM-64)
    */
-  AL2_ARM_64 = 'AL2_ARM_64'
+  AL2_ARM_64 = 'AL2_ARM_64',
+  /**
+   *  Bottlerocket Linux(ARM-64)
+   */
+  BOTTLEROCKET_ARM_64 = 'BOTTLEROCKET_ARM_64',
+  /**
+   * Bottlerocket(x86-64)
+   */
+  BOTTLEROCKET_X86_64 = 'BOTTLEROCKET_x86_64',
 }
 
 /**