Task: Integrate Agent Server sleep restart fix

Identity

Merge exact feature commit 12d7588c into local main.
Preserve the already-integrated model-reasoning capability behavior.
Record the integration in canonical current state without changing Pi, Provider, packaging, or replay contracts.

Pi 0.84.2 remains the sole Coding runtime and one Main-owned Agent Server remains the parent topology.
Background sleep must not stop work that begins during cleanup, and start racing stop must create one fresh server after stop settles.
Accepted and uncertain prompts must never be replayed automatically.
Stop on any merge conflict or semantic conflict; do not choose by merge order.
Do not package, install, deploy, push, or change dependencies in this integration task.

Verify the exact source commit and a conflict-free merge tree against current main.
Merge the source branch with an explicit merge commit.
Record the integrated behavior and remaining installed-package gate in canonical current state.
Run focused lifecycle tests, typecheck, lint, production build, and documentation drift checks.
Commit integration memory, complete the task, and release ownership from a clean worktree.

Verified source commit 12d7588b3ebd4d192c2e14ae285d4f6ddebeeb42 and conflict-free merge tree 63750df00cda0da00304725b6f0a8c17dd5e09b0 against current main.
Merged the exact source into local main as c2137c9f3f2e05441064cc90bfeed115363ac04e without conflict.
Preserved the already-integrated model-reasoning capability changes and the Pi 0.84.2 single-Agent-Server architecture.
Recorded the background-sleep recheck and serialized stop/start behavior in canonical current state.
No package, installation, deployment, push, dependency, Provider, or replay-contract change was performed.

git merge-tree --write-tree HEAD 12d7588 returned conflict-free tree 63750df00cda0da00304725b6f0a8c17dd5e09b0 before merge.
Merged-main focused lifecycle run: 4 files / 9 tests passed.
pnpm run typecheck: passed.
pnpm run lint:check: zero errors and the repository's existing five warnings.
pnpm test: 216 files passed; 1,780 tests passed and 2 skipped.
pnpm run build:vite: Renderer, Electron Main, Preload, and utility production builds passed with existing build warnings only.

Build, verify, and reinstall a Windows package from integrated main, then repeat the reported prompt-after-idle interaction. The currently installed application still contains the old lifecycle code.

Resolved: recorded the exact source and merge commits, lifecycle behavior, no-replay invariant, and remaining installed-package gate in .project-docs/30-worklog/current-state.md. No ADR or architecture rewrite was needed because the fix enforces ADR-006.