Hi
I will try to clarify things as I understand it.
The Docker compose file is provided by Camunda to make local development easy. You are not allowed to create a production setup using the Docker compose file and all the components used without a Camunda license.
As far as I recall, the only Camunda component you are allow to use without a license from Camunda is the Zeebe component (and there are limitations on that, so check the Zeebe license).
So to create a valid production setup without a Camunda license, you would then use the Zeebe broker(s) running either on a Kubernetes cluster, using Docker containers or as a local installation (Camunda Platform 8 deployment | Camunda Platform 8). You then need - some - access to the process instances / tasks to create your own tasklist. The Zeebe broker does not have a GraphQL API. You need to export the process data from the Zeebe brokers using the an exporter. You can use the Elasticsearch exporter, but a Hazelcast exporter is created by the community. That may also be an option.
Hope that helps.
BR
Michael