Background agent sessions should be fully exportable and inspectable

[brycecutt-msft]

Describe the feature or problem you'd like to solve

background agents launched via the task tool don't persist their tool calls or outputs. /share captures reasoning blocks but not the actual grep, edit, and shell commands. /tasks empties once agents complete. session store database has no record of the subtask. you can follow the agent's thinking but can't verify its actions.

Proposed solution

1. persist completed background agent sessions as inspectable child sessions linked to the parent
2. /tasks should list completed agents (not just running ones) with their session ids
3. /share should include subagent tool calls and outputs (inline or as linked sections) - currently only reasoning blocks are captured
4. /resume should allow browsing a completed agent's full conversation read-only
5. alternatively, a /share --include-subtasks flag for full recursive export

Example prompts or workflows

1. launch a background agent that modifies multiple files, creates a branch, and opens a PR. after it completes, try to inspect what it actually did step by step - you can't
2. /share after a session with background agents - the export shows the agent's reasoning but not its tool invocations or their outputs
3. /tasks after a background agent finishes - empty list, no way to get back to it

Additional context

No response