[Feature]: SAM CLI durable emulator integration tests are ported to this repository

### What would you like?

Context: Changes to the `aws-durable-execution-sdk-python` and `aws-durable-execution-sdk-python-testing` can often break assertions in the SAM CLI integration tests:

1. https://github.com/aws/aws-sam-cli/pull/8906
2. https://github.com/aws/aws-sam-cli/actions/runs/28089573325/job/83163914199

At the time of writing these tests in SAM CLI, the intention was to test the emulator behaviour. Now that we automatically publish an emulator image for SAM CLI from this repository, I think we can loosen some of the tests on SAM CLI side. SAM CLI doesn't need to test the specifics of our SDK behaviour, only that durable functions can be run and that the execution history can be fetched in SAM CLI. The specific behaviour of the published emulator image in conjunction with the Python SDK (such as the presence of certain fields in the execution history) can be tested in this repository rather than in SAM CLI.

We want to have stronger ownership over our SAM CLI integration as well as reduce churn for SAM CLI owners.

### Possible Implementation

1. Check emulator image test coverage in current repository
2. Check emulator image test coverage in SAM CLI
3. Reason over tests we can keep in SAM and tests we can port (define how decoupled we want to be between the durable emulator image and SAM CLI, decide minimum functionality we want to test on SAM side)
4. Port over relevant tests to current repository that we are missing
5. Remove relevant tests from SAM CLI
### Is this a breaking change?

No

### Does this require an RFC?

No

### Additional Context

This is really similar to https://github.com/aws/aws-durable-execution-sdk-python/issues/430. We could consider porting these tests and running them via the SAM CLI for this issue as well.

まず、このリポジトリのエミュレーターイメージのテストカバレッジを SAM CLI の統合テストと比較し、リンクされた SAM CLI のプルリクエストとワークフロー実行を参照してください。保持すべき SAM CLI の最小限の動作を定義し、ここに不足しているエミュレーター固有のカバレッジを移植して、durable-function の実行と履歴のカバレッジを失うことなく SAM CLI のテストを削減できることを検証してください。

索引モデルが issue の本文から書いたものです。