[FEATURE] Allow restoring background task shell access from SDK so the Agent can KillShell for a session id still.

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When the Agent launches a sub process if we terminate and relaunch the application the Agent session restores but we no longer have access to background tasks, resulting in

<tool_use_error>No shell found with ID: bcf8f19</tool_use_error>

errors, since we're restoring a session I believe that the SDK should also be able to recover its background process context.

Proposed Solution

Agents restore Shell environments associated to a SessionID when a thread comes back to life.

Alternative Solutions

Expose an SDK first party background process poller (isTaskAlive, isTaskAvailableToContext) so Agent SDK can properly determine _real state_ for the Session.

Priority

High - Significant impact on productivity

Feature Category

CLI commands and flags

Use Case Example

Ask the agent to launch a program.
Close the agent on accident, or from a crash, or anything really.
Relaunch
Agent regains context of background processes properly.
Ask agent to close the program.
Program launched properly closes.

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This avoids runaway background tasks as-well.
Improves DX from having to maintain a process list and session map.

Additional Context

https://github.com/user-attachments/assets/0e9f8c88-c30f-4e30-9431-c9899e6c2921