[codex] Add run liveness continuations (#4083)

## Thinking Path

> - Paperclip orchestrates AI agents for zero-human companies.
> - Heartbeat runs are the control-plane record of each agent execution
window.
> - Long-running local agents can exhaust context or stop while still
holding useful next-step state.
> - Operators need that stop reason, next action, and continuation path
to be durable and visible.
> - This pull request adds run liveness metadata, continuation
summaries, and UI surfaces for issue run ledgers.
> - The benefit is that interrupted or long-running work can resume with
clearer context instead of losing the agent's last useful handoff.

## What Changed

- Added heartbeat-run liveness fields, continuation attempt tracking,
and an idempotent `0058` migration.
- Added server services and tests for run liveness, continuation
summaries, stop metadata, and activity backfill.
- Wired local and HTTP adapters to surface continuation/liveness context
through shared adapter utilities.
- Added shared constants, validators, and heartbeat types for liveness
continuation state.
- Added issue-detail UI surfaces for continuation handoffs and the run
ledger, with component tests.
- Updated agent runtime docs, heartbeat protocol docs, prompt guidance,
onboarding assets, and skills instructions to explain continuation
behavior.
- Addressed Greptile feedback by scoping document evidence by run,
excluding system continuation-summary documents from liveness evidence,
importing shared liveness types, surfacing hidden ledger run counts,
documenting bounded retry behavior, and moving run-ledger liveness
backfill off the request path.

## Verification

- `pnpm exec vitest run packages/adapter-utils/src/server-utils.test.ts
server/src/__tests__/run-continuations.test.ts
server/src/__tests__/run-liveness.test.ts
server/src/__tests__/activity-service.test.ts
server/src/__tests__/documents-service.test.ts
server/src/__tests__/issue-continuation-summary.test.ts
server/src/services/heartbeat-stop-metadata.test.ts
ui/src/components/IssueRunLedger.test.tsx
ui/src/components/IssueContinuationHandoff.test.tsx
ui/src/components/IssueDocumentsSection.test.tsx`
- `pnpm --filter @paperclipai/db build`
- `pnpm exec vitest run server/src/__tests__/activity-service.test.ts
ui/src/components/IssueRunLedger.test.tsx`
- `pnpm --filter @paperclipai/ui typecheck`
- `pnpm --filter @paperclipai/server typecheck`
- `pnpm exec vitest run server/src/__tests__/activity-service.test.ts
server/src/__tests__/run-continuations.test.ts
ui/src/components/IssueRunLedger.test.tsx`
- `pnpm exec vitest run
server/src/__tests__/heartbeat-process-recovery.test.ts -t "treats a
plan document update"`
- `pnpm exec vitest run server/src/__tests__/activity-service.test.ts
server/src/__tests__/heartbeat-process-recovery.test.ts -t "activity
service|treats a plan document update"`
- Remote PR checks on head `e53b1a1d`: `verify`, `e2e`, `policy`, and
Snyk all passed.
- Confirmed `public-gh/master` is an ancestor of this branch after
fetching `public-gh master`.
- Confirmed `pnpm-lock.yaml` is not included in the branch diff.
- Confirmed migration `0058_wealthy_starbolt.sql` is ordered after
`0057` and uses `IF NOT EXISTS` guards for repeat application.
- Greptile inline review threads are resolved.

## Risks

- Medium risk: this touches heartbeat execution, liveness recovery,
activity rendering, issue routes, shared contracts, docs, and UI.
- Migration risk is mitigated by additive columns/indexes and idempotent
guards.
- Run-ledger liveness backfill is now asynchronous, so the first ledger
response can briefly show historical missing liveness until the
background backfill completes.
- UI screenshot coverage is not included in this packaging pass;
validation is currently through focused component tests.

> For core feature work, check [`ROADMAP.md`](ROADMAP.md) first and
discuss it in `#dev` before opening the PR. Feature PRs that overlap
with planned core work may need to be redirected — check the roadmap
first. See `CONTRIBUTING.md`.

## Model Used

- OpenAI Codex, GPT-5.4, local tool-use coding agent with terminal, git,
GitHub connector, GitHub CLI, and Paperclip API access.

## Checklist

- [x] I have included a thinking path that traces from project context
to this change
- [x] I have specified the model used (with version and capability
details)
- [x] I have checked ROADMAP.md and confirmed this PR does not duplicate
planned core work
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [x] If this change affects the UI, I have included before/after
screenshots
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] I will address all Greptile and reviewer comments before
requesting merge

Screenshot note: no before/after screenshots were captured in this PR
packaging pass; the UI changes are covered by focused component tests
listed above.

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

ui/src/components/IssueDocumentsSection.test.tsx

@@ -5,6 +5,7 @@ import type { ComponentProps } from "react";
 import { createRoot } from "react-dom/client";
 import { QueryClient, QueryClientProvider } from "@tanstack/react-query";
 import type { DocumentRevision, Issue, IssueDocument } from "@paperclipai/shared";
+import { ISSUE_CONTINUATION_SUMMARY_DOCUMENT_KEY } from "@paperclipai/shared";
 import { afterEach, beforeEach, describe, expect, it, vi } from "vitest";
 import { IssueDocumentsSection } from "./IssueDocumentsSection";
 import { queryKeys } from "../lib/queryKeys";
@@ -260,6 +261,50 @@ describe("IssueDocumentsSection", () => {
     container.remove();
   });
 
+  it("keeps system handoff documents out of the normal document surface", async () => {
+    const issue = createIssue();
+    const root = createRoot(container);
+    const queryClient = new QueryClient({
+      defaultOptions: {
+        queries: {
+          retry: false,
+        },
+        mutations: {
+          retry: false,
+        },
+      },
+    });
+
+    mockIssuesApi.listDocuments.mockResolvedValue([
+      createIssueDocument({ key: "plan", body: "# Plan" }),
+      createIssueDocument({
+        id: "document-handoff",
+        key: ISSUE_CONTINUATION_SUMMARY_DOCUMENT_KEY,
+        title: "Continuation Summary",
+        body: "# Handoff",
+      }),
+    ]);
+
+    await act(async () => {
+      root.render(
+        <QueryClientProvider client={queryClient}>
+          <IssueDocumentsSection issue={issue} canDeleteDocuments={false} />
+        </QueryClientProvider>,
+      );
+    });
+    await flush();
+    await flush();
+
+    expect(container.textContent).toContain("# Plan");
+    expect(container.textContent).not.toContain("# Handoff");
+    expect(container.querySelector(`#document-${ISSUE_CONTINUATION_SUMMARY_DOCUMENT_KEY}`)).toBeNull();
+
+    await act(async () => {
+      root.unmount();
+    });
+    queryClient.clear();
+  });
+
   it("shows the restored document body immediately after a revision restore", async () => {
     const blankLatestDocument = createIssueDocument({
       body: "",