[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>

server/src/services/documents.ts

@@ -1,7 +1,7 @@
 import { and, asc, desc, eq } from "drizzle-orm";
 import type { Db } from "@paperclipai/db";
 import { documentRevisions, documents, issueDocuments, issues } from "@paperclipai/db";
-import { issueDocumentKeySchema } from "@paperclipai/shared";
+import { isSystemIssueDocumentKey, issueDocumentKeySchema } from "@paperclipai/shared";
 import { conflict, notFound, unprocessable } from "../errors.js";
 
 function normalizeDocumentKey(key: string) {
@@ -83,8 +83,14 @@ const issueDocumentSelect = {
 };
 
 export function documentService(db: Db) {
+  const filterSystemDocuments = <T extends { key: string }>(rows: T[], includeSystem: boolean) =>
+    includeSystem ? rows : rows.filter((row) => !isSystemIssueDocumentKey(row.key));
+
   return {
-    getIssueDocumentPayload: async (issue: { id: string; description: string | null }) => {
+    getIssueDocumentPayload: async (
+      issue: { id: string; description: string | null },
+      options: { includeSystem?: boolean } = {},
+    ) => {
       const [planDocument, documentSummaries] = await Promise.all([
         db
           .select(issueDocumentSelect)
@@ -104,7 +110,8 @@ export function documentService(db: Db) {
 
       return {
         planDocument: planDocument ? mapIssueDocumentRow(planDocument, true) : null,
-        documentSummaries: documentSummaries.map((row) => mapIssueDocumentRow(row, false)),
+        documentSummaries: filterSystemDocuments(documentSummaries, options.includeSystem ?? false)
+          .map((row) => mapIssueDocumentRow(row, false)),
         legacyPlanDocument: legacyPlanBody
           ? {
               key: "plan" as const,
@@ -115,14 +122,14 @@ export function documentService(db: Db) {
       };
     },
 
-    listIssueDocuments: async (issueId: string) => {
+    listIssueDocuments: async (issueId: string, options: { includeSystem?: boolean } = {}) => {
       const rows = await db
         .select(issueDocumentSelect)
         .from(issueDocuments)
         .innerJoin(documents, eq(issueDocuments.documentId, documents.id))
         .where(eq(issueDocuments.issueId, issueId))
         .orderBy(asc(issueDocuments.key), desc(documents.updatedAt));
-      return rows.map((row) => mapIssueDocumentRow(row, true));
+      return filterSystemDocuments(rows, options.includeSystem ?? false).map((row) => mapIssueDocumentRow(row, true));
     },
 
     getIssueDocumentByKey: async (issueId: string, rawKey: string) => {