Configure cluster management regions using secrets/variables

> I don't think we need to change this right now, but I think we should probably move [cluster management] regions to Github secrets/variables to avoid duplication between this file and the examples themselves.

_Originally posted by @mitchell-elholm in https://github.com/aws-samples/aurora-dsql-samples/pull/144#discussion_r2093744425_

There are several places where we reference the regions `us-east-1` and `us-east-2` in the context of the cluster management examples. We are currently choosing to run the tests for all languages against these regions, but may want to change that in the future.

We should define these regions using secrets/variables in the workflow files, so we can easily change them and centralize their definition.

Places to update:
- Workflow files
- `clean-cluster.sh` script
- Cluster management tests

The cluster management tests allow configuration through environment variables in most cases. We may need to double check that they all do, but if not this should be a small change. Then we can configure the regions to use environment variables in the workflows for the test runs.

Locate the workflow files, clean-cluster.sh, and the cluster management tests mentioned in the issue. First check how each test accepts region configuration through environment variables, then trace the current us-east-1 and us-east-2 references. Done means the regions have one workflow-level secrets/variables definition and all listed workflows, the script, and tests use it without duplicated region values.

Written by the indexing model from the issue text.