[BUG] StrandsA2AExecutor served via serve_a2a never hits AgentCore idle session timeout (causes runaway execution environments)

### SDK Language

Python

### Strands Version

strands-agents[otel,a2a]==1.45.0

### Language Runtime Version

Python 3.13

### Operating System

python:3.13-slim-bookworm docker image running in agentcore runtime

### Installation Method

other

### Steps to Reproduce

- Create a minimal vanilla Strands agent using the bedrock-agentcore-sdk-python and strands-agents SDKs.
- Wrap the agent using StrandsA2AExecutor(..., enable_a2a_compliant_streaming=True) and serve it using serve_a2a().
- Deploy the application to an AWS Bedrock AgentCore Runtime.
- Invoke the agent normally.
- Monitor the AWS CloudWatch metrics and log streams for the execution environment.

```python
import os

from bedrock_agentcore.runtime import serve_a2a
from strands import Agent
from strands.models.bedrock import BedrockModel
from strands.multiagent.a2a.executor import StrandsA2AExecutor

_MODEL_ID = os.getenv("MODEL_ID", "")
_AGENT_CARD_CONTEXT_ID = "__agent_card__"
_AGENT_DESCRIPTION = (
"An analytics agent"
)
_SYSTEM_PROMPT = (
"You are an analytics assistant."
)

def _build_agent() -> Agent:
return Agent(
model=BedrockModel(model_id=_MODEL_ID),
name="Agent",
description=_AGENT_DESCRIPTION,
system_prompt=_SYSTEM_PROMPT,
)

def _agent_factory(context_id: str) -> Agent:
return _build_agent()

if __name__ == "__main__":
executor = StrandsA2AExecutor(
agent_factory=_agent_factory,
enable_a2a_compliant_streaming=True,
)
serve_a2a(executor)

```

### Expected Behavior

After the client request finishes (or the client disconnects), the underlying ASGI server should cleanly resolve the request. The AgentCore Runtime should then recognize the environment as "Idle", start the idleRuntimeSessionTimeout countdown, and cleanly shut down the microVM once the timeout is reached.

### Actual Behavior

- The AgentCore Runtime considers the environment continuously "Active".
- The idleRuntimeSessionTimeout is never reached.
- Despite there being no further requests for the session, the execution environment remains alive, indefinitely racking up continuous GB-hour billing, until it hits the platform's absolute hard maximum lifetime limit (e.g., 8 hours) and is forcefully killed.

### Additional Context

I don't have the same issue for regular (non-A2A) strands agents.

I originally opened a bug report to the Strands developers https://github.com/strands-agents/harness-sdk/issues/3120 and they said they internally diverted it to the agentcore team. I am making this ticket so there is a publicly accessible way to track the progress.

### Possible Solution

_No response_

### Related Issues

_No response_

serve_a2a() エントリポイントと enable_a2a_compliant_streaming=True で設定された StrandsA2AExecutor から始め、AWS Bedrock AgentCore でリクエスト完了とクライアント切断のパスを再現します。CloudWatch のメトリクスとログストリームを使用して、環境が Idle になり、リクエスト終了後に idleRuntimeSessionTimeout によってシャットダウンできることを確認します。

索引モデルが issue の本文から書いたものです。