Don't overlook SSM <https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/session-...> which doesn't require sshd nor public access to get onto a machine and one can opt in to a bunch of audit logging if that's your jam. They also have some "ansible-y" behavior about running playbooks against groups of instances, but I haven't had good experiences with that process in order to recommend it. It's just a small bonus that one can also hop onto an instance from the AWS Console when using SSM, since it is websocket based and not "ssh from the browser"

The agent is Apache 2 if one wanted to build, enhance, or audit what it does: https://github.com/aws/amazon-ssm-agent#readme as is the local binary that awscli uses for the websocket handshaking: https://github.com/aws/session-manager-plugin#readme