Managed zookeeper or etcd offering

AWS does not currently offer a dedicated managed service specifically for Apache ZooKeeper or etcd. However, there are several options available for running these coordination services on AWS:

For Apache ZooKeeper:

• Amazon EMR includes Apache ZooKeeper as a component. The latest EMR 7.x series includes ZooKeeper 3.9.3, while EMR 6.x series includes ZooKeeper 3.5.10. When you deploy ZooKeeper through EMR, it comes with various components like hadoop-client, zookeeper-client, zookeeper-server, and other related services.

For service mesh requirements:

• AWS App Mesh is a managed service mesh offering that provides consistent visibility and network traffic controls for services. It's a fully managed and highly available service that allows you to manage service communications without needing to install or manage application-level infrastructure for communications management.

If the customer is specifically looking for coordination services like ZooKeeper or etcd for their service mesh implementation, they would need to deploy and manage these services themselves on AWS infrastructure such as EC2 instances or containers, as there is no dedicated managed offering specifically for these coordination services outside of EMR for ZooKeeper.
Sources
AWS App Mesh Features - Amazon Web Services
Apache ZooKeeper - Amazon EMR
ZooKeeper release history - Amazon EMR