Check the Amazon image version of your EC2 instance.

Command: cat /etc/image-id

If it is Amazon Linux 2023, it does not have extras.

However, most of the packages are already included in the distro.

You can run sudo yum install nginx which will install version 1.22

From Amazon Linux 2023 FAQ :

Q: Does AL2023 have Amazon-Linux-Extras like AL2?

A: No, AL2023 does not have extras. For higher-level software packages like language runtimes, we will use the quarterly release where we will add major/minor updates to packages as separate namespaced packages in addition to the default package provided in the repository. For example, default Python version in Amazon Linux 2023 may be 3.8, but we will add Python 3.9 (python39) as a separate namespaced package whenever it is made available. These additional packages will closely follow their upstream release cadence and support model and their support policies can be accessed by the package manager for compliance and security use cases. Default packages will continue to be supported throughout the life of AL2023.

This explains your problem - amazon-linux-extras doesn't exist in Amazon Linux 2023, although it existed in Amazon Linux 2.

I ran into the same error message when attempting to create an Amazon Linux 2 instance using the AWS CDK. The CDK currently defaults to Amazon Linux instead of Amazon Linux 2. When you accidentally use an Amazon Linux AMI from 2018, surprise surprise, all sorts of facilities are not available. I posted an easy way to check your version in another answer.

In CDK (and Cloud Formation) make sure to declare your intended generation in your AmazonLinuxImage properties

generation: AmazonLinuxGeneration.AMAZON_LINUX_2

Install Docker

sudo yum update -y
sudo yum -y install docker

Start Docker

sudo service docker start

Access Docker commands in ec2-user user

sudo usermod -a -G docker ec2-user
sudo chmod 666 /var/run/docker.sock
docker version