Sorry i didn't add the disclaimer that I haven't used MWAA. I had used airflow (cloud composer) on GCP which was running inside a k8s cluster and we used to push docker image to our private docker repo during CI/CD. Then you can use kubernetes pod operator.
I googled around for docker support for MWAA and I found this
https://medium.com/@sohflp/how-to-work-with-airflow-docker-operator-in-amazon-mwaa-5c6b7ad36976