Add end-to-end testing with backend deployment to integration tests workflow

[rarepolz]

Context

The current integration tests workflow runs unit tests and example tests from the testing SDK, but we need to add end-to-end testing by deploying and running examples against the actual backend infrastructure.

This would provide comprehensive validation that Language SDK changes work correctly in real AWS environments, not just in isolated test scenarios.

Technical Requirements

• Extend the existing integration tests workflow to include deployment and execution of examples
• Deploy examples to AWS backend infrastructure
• Run end-to-end tests against deployed examples
• Follow the pattern established in the testing SDK's deploy-examples workflow

Implementation Details

Files to modify:

• .github/workflows/integration-tests.yml - extend existing workflow
• Reference implementation: https://github.com/aws/aws-durable-execution-sdk-python-testing/blob/main/.github/workflows/deploy-examples.yml

Key components:

• AWS credentials setup for deployment
• Example deployment step using testing SDK tooling
• End-to-end test execution against deployed backend
• Cleanup of deployed resources

Acceptance Criteria

• Integration tests workflow deploys examples to AWS backend
• End-to-end tests run against deployed examples
• Tests validate Language SDK changes work in real AWS environment
• Deployed resources are properly cleaned up after testing
• Workflow maintains existing unit test and example test coverage

Priority: High
Estimated Effort: 0.5 days

Originally posted by @bchampp in #62 (review)

Merged the previous PR. However, there are some issues with parsing.

I'd rather we use python scripts or nodejs scripts if possible.