[Feature]: [Testing] Emulator should generate real-shaped durable execution ARNs (embed execution name)

### What would you like?

### Context

Reported downstream in [aws/aws-sam-cli#9200](https://github.com/aws/aws-sam-cli/issues/9200): a user who starts a local durable execution with `sam local invoke --durable-execution-name test` cannot correlate that name with anything afterwards — `sam local execution history/get` take an ARN, and the emulator's ARN contains no trace of the name.

### Current behavior

The emulator generates a placeholder ARN in `Execution.new()` ([execution.py](https://github.com/aws/aws-durable-execution-sdk-python/blob/main/packages/aws-durable-execution-sdk-python-testing/src/aws_durable_execution_sdk_python_testing/execution.py#L185)):

```python
# make a nicer arn
# Pattern: arn:(aws[a-zA-Z-]*)?:lambda:...:durable-execution:...
return Execution(
durable_execution_arn=str(uuid4()) + "/" + (input.invocation_id or str(uuid4())),
...
)
```

Two problems:

1. It doesn't match the real service ARN shape, so the execution name (and function name) appear nowhere in the identifier. Locally, `DurableExecutionName` is effectively write-only.
2. It conflates the second path segment with the *invocation* ID; the real ARN's last segment is a distinct execution ID.

(The comment's intended pattern is also stale — it predates the current public API shape.)

### Expected behavior

Generate ARNs matching the public `DurableExecutionArn` pattern from the Lambda service model:

```
arn:{partition}:lambda:{region}:{account}:function:{name}:{qualifier}/durable-execution/{execution-name}/{execution-id}
```

Everything needed is already on `StartDurableExecutionInput` (`account_id`, `function_name`, `function_qualifier`, `execution_name` are required fields). Region can be fixed to `us-east-1`, consistent with the hardcoded `FunctionArn` in `executor.py`'s `GetDurableExecution` response.

### Possible Implementation

- **Null/omitted execution name:** callers (e.g. SAM CLI) may send `"ExecutionName": null`. Generate a name (uuid) when absent — matches cloud behavior and also fixes `DurableExecutionName` being null in `GetDurableExecution` responses.
- **Execution ID:** use a fresh `uuid4()`, not `invocation_id`.
- **Routing is already safe:** `Route.from_string` splits on `/` before URL-decoding, so a percent-encoded ARN stays one segment — the same mechanism that handles today's one-slash placeholder. botocore percent-encodes `/` in non-greedy URI params.
- **Downstream (sam-cli) is already shape-agnostic** after aws/aws-sam-cli#9038 and aws/aws-sam-cli#9040 (`\S+` ARN regex, Flask `` routes).
- Store/runner treat the ARN as an opaque key; only tests asserting the placeholder shape need updating.

**Questions to resolve:**

- **Execution-name idempotency:** mimic cloud idempotency behaviour — in the service, starting a durable execution with an `ExecutionName` that matches an existing execution for the same function is an idempotent start (the existing execution/ARN is returned rather than a new one created). The emulator currently creates a duplicate with a distinct ARN sharing the same name segment. Confirm the exact service semantics (idempotency window, retention, input-mismatch handling) and implement to match.
- **Function name fidelity:** SAM CLI hardcodes `"FunctionName": "function"` in its start payload, so local ARNs would read `function:function:$LATEST/...`. Decide whether to pair this with a sam-cli change to pass the real logical ID so the ARN is actually informative.

### Blocked by

A new emulator image release is required for this to reach SAM CLI users (`:latest` on ECR is still v1.2.1, built 2026-05-20 from the pre-migration repo) — see #487.

Start in packages/aws-durable-execution-sdk-python-testing/src/aws_durable_execution_sdk_python_testing/execution.py at Execution.new(), then inspect executor.py's GetDurableExecution response and Route.from_string. Update tests that assert the placeholder ARN shape, and verify generated ARNs include the required function, qualifier, execution name, and fresh execution ID while absent names are handled consistently.

Written by the indexing model from the issue text.