Migrate JavaScript SDK CI tests to SAM

- Migrate the test deployment mechanism from the custom script to SAM CLI (sam build + sam deploy).
- Validate for both Node 22.x and 24.x runtimes, clean up JS test functions from old resource and document if required.

Start by locating the custom CI test deployment script and the JavaScript test functions that provision the old resources. Compare their flow with SAM CLI’s sam build and sam deploy, then validate the deployment for Node 22.x and 24.x. Done means the old resources are removed, both runtimes pass, and any needed documentation is updated.

Written by the indexing model from the issue text.