Background agent sessions should be fully exportable and inspectable

### 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_

Start by tracing the /tasks, /share, and /resume entry points and the session store database behavior for completed background agents. Define how child sessions and their tool calls and outputs are persisted, listed, exported, and browsed read-only; done means the workflows in the issue can inspect completed agents and their actions.

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