After switching the alternate secrets backend to the Parameter store I was able to retrieve connections/variables from the SSM Parameter store, but the only issue was the task logs page in the Airflow webserver UI was stuck in a loading state. I can still view task logs from the Cloudwatch portal.
Airflow config
secrets.backend airflow.providers.amazon.aws.secrets.systems_manager.SystemsManagerParameterStoreBackend
secrets.backend_kwargs {"connections_prefix" : "airflow/connections", "variables_prefix" : "airflow/variables"}
SystemsManager policy attached to execution role
{
"Version": "2012-10-17",
"Statement": [
{
"Sid": "VisualEditor0",
"Effect": "Allow",
"Action": "ssm:*",
"Resource": "arn:aws:ssm:us-east-1:<account_id>:parameter/airflow*"
}
]
}