Completed worktree sessions leave Copilot CLI processes and stale background activity on Windows

## Summary

On Windows, completed worktree-backed sessions can leave their per-session `copilot.exe --server --stdio` process running after the PR is merged and the worktree directory has already been cleaned. The process retains a worktree handle, can make archival fail with Windows `os error 32`, and Background activity can show checks as running when no agent or test process exists.

Reproduced across three independent completed sessions and during a larger child-session cleanup.

## Environment

- GitHub Copilot App **1.1.12**
- Agency **2026.8.21.9**
- Copilot CLI **1.0.80**
- Windows 11 Enterprise Insider Preview **10.0.29648** (build **29648**)
- Local worktree-backed sessions
- Observed 2026-08-24/25

## Evidence

Three sessions had merged PRs whose exact heads were ancestors of `origin/master`. Their worktree directories existed but had zero entries and no `.git`. Each still had one Copilot CLI server referencing the removed worktree:

```text
\github-copilot-sdk\cli\1.0.80\copilot.exe
--server --stdio --add-dir ...
```

Residual PIDs observed: `86828`, `134332`, `139508` (ephemeral, for correlation only).

An archive attempt also failed repeatedly with:

```text
Failed to archive session: The process cannot access the file because it is being used by another process. (os error 32)
```

Sysinternals Handle identified:

```text
github.exe pid 61856 File handle 1C08
copilot.exe pid 144316 File handle 5C
```

After stopping only PID `144316`, the app released its handle and the same archive operation succeeded. Sequential archival then succeeded for every session. The process did not respawn.

The app also showed these as active:

```text
Run full exact-SHA local gate
Run exact-SHA fabricated browser proof
```

Independent inspection showed zero running agents, only an idle Scribe, all shell tasks completed, and no matching Node/npm/Playwright/browser-test process.

## Log evidence

Raw logs are not attached because they contain local paths, MCP metadata, and conversation/tool payloads. Redacted inventory:

| Case | Agency log | Copilot process log |
|---|---:|---:|
| Completed A | 484,099 B | 69,644,142 B |
| Completed B | 343,884 B | 24,139,171 B |
| Completed C | 454,435 B | 131,400,825 B |
| Archive lock | 95,181 B | 985,924 B |

Each completed-session Agency log records Working directory, Adding git root to `--add-dir`, and Executing copilot command with `--server --stdio --add-dir `. No corresponding shutdown, EOF, process-exit, or termination event was found. Logs end with periodic activity:

```text
telem periodic flush: queue empty, nothing to commit
accepted OTLP signal (not yet processed) signal=/v1/metrics
```

One affected log contains repeated `archive_session` traces but no matching CLI shutdown.

## Reproduction

1. Create a local worktree-backed session on Windows.
2. Complete work and merge its PR.
3. Allow the app to clean the worktree while the session record remains visible.
4. Inspect `copilot.exe` command lines for `--server --stdio --add-dir `.
5. Attempt to archive the session, especially with other sessions.
6. Observe `os error 32` or a retained process/handle.
7. Stop the exact per-session Copilot PID and retry; archival succeeds.

## Expected

- Archive terminates and awaits the per-session CLI, releases handles, removes the worktree, then marks the session archived atomically.
- Completed background tasks leave the running section even if a worker exits unexpectedly.
- If retaining an unarchived runtime is intentional, show it as idle and ensure archive closes it reliably.

## Actual

- Completed/merged sessions can retain a Copilot CLI indefinitely.
- The CLI and GitHub App can retain worktree directory handles.
- Archive can fail on its own retained handles with `os error 32`.
- Background activity can show running tasks with no corresponding agent or OS process.

## Workaround

Find the exact process associated with the worktree and stop only that PID, then archive sequentially:

```powershell
Stop-Process -Id
```

Do not terminate all processes by name because other sessions use the same executable.

All user paths, repository details, plugin IDs, MCP filenames, and conversation content are redacted. Full logs can be provided through a private diagnostic channel.

Start by reproducing the Windows worktree-backed session lifecycle and inspect per-session `copilot.exe --server --stdio --add-dir ` processes during archival. Trace archive handling and completed background activity until the CLI is terminated and awaited, handles are released, stale tasks leave the running section, and archival succeeds without `os error 32`.

Written by the indexing model from the issue text.