The issue appears to affect users who have a newer version of Ubuntu. If you have Ubuntu 20.04 or older installed, you should not be experiencing this.
Workaround:
To fix it, you need to pass the Ubuntu 20 AMI for your region, to the --amazonec2-ami argument for docker-machine. The resulting command is looking like this:
docker-machine create --driver amazonec2 --amazonec2-root-size 16 --amazonec2-instance-type t3.large --amazonec2-ami ami-04505e74c0741db8d $env:DOCKER_MACHINE_NAME
You can find the AMI ID by searching for Ubuntu in the AWS Console:
More information about the bug can be found here: https://gitlab.com/gitlab-org/gitlab-runner/-/issues/29029