1Password connect on AWS ECS without public network - is it possible

I am using yml provided here https://github.com/1Password/connect/blob/main/examples/aws-ecs-fargate/connect.yaml to build 1Password connect stack on AWS, this all works nicely, however, I was wondering if I can somehow do the same but without public access to the API, so that only other vpcs within the same aws account can query it?

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