[codex] Harden heartbeat scheduling and runtime controls (#4223)

## Thinking Path

> - Paperclip orchestrates AI agents through issue checkout, heartbeat
runs, routines, and auditable control-plane state
> - The runtime path has to recover from lost local processes, transient
adapter failures, blocked dependencies, and routine coalescing without
stranding work
> - The existing branch carried several reliability fixes across
heartbeat scheduling, issue runtime controls, routine dispatch, and
operator-facing run state
> - These changes belong together because they share backend contracts,
migrations, and runtime status semantics
> - This pull request groups the control-plane/runtime slice so it can
merge independently from board UI polish and adapter sandbox work
> - The benefit is safer heartbeat recovery, clearer runtime controls,
and more predictable recurring execution behavior

## What Changed

- Adds bounded heartbeat retry scheduling, scheduled retry state, and
Codex transient failure recovery handling.
- Tightens heartbeat process recovery, blocker wake behavior, issue
comment wake handling, routine dispatch coalescing, and
activity/dashboard bounds.
- Adds runtime-control MCP tools and Paperclip skill docs for issue
workspace runtime management.
- Adds migrations `0061_lively_thor_girl.sql` and
`0062_routine_run_dispatch_fingerprint.sql`.
- Surfaces retry state in run ledger/agent UI and keeps related shared
types synchronized.

## Verification

- `pnpm exec vitest run
server/src/__tests__/heartbeat-retry-scheduling.test.ts
server/src/__tests__/heartbeat-process-recovery.test.ts
server/src/__tests__/routines-service.test.ts`
- `pnpm exec vitest run src/tools.test.ts` from `packages/mcp-server`

## Risks

- Medium risk: this touches heartbeat recovery and routine dispatch,
which are central execution paths.
- Migration order matters if split branches land out of order: merge
this PR before branches that assume the new runtime/routine fields.
- Runtime retry behavior should be watched in CI and in local operator
smoke tests because it changes how transient failures are resumed.

> 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-based coding agent runtime, shell/git tool use
enabled. Exact hosted model build and context window are not exposed in
this Paperclip heartbeat environment.

## 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
- [ ] 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

server/src/__tests__/activity-service.test.ts

@@ -1,6 +1,7 @@
 import { randomUUID } from "node:crypto";
 import { afterAll, afterEach, beforeAll, describe, expect, it } from "vitest";
 import {
+  activityLog,
   agents,
   companies,
   createDb,
@@ -56,6 +57,7 @@ describeEmbeddedPostgres("activity service", () => {
   }, 20_000);
 
   afterEach(async () => {
+    await db.delete(activityLog);
     await db.delete(issueComments);
     await db.delete(issueDocuments);
     await db.delete(documentRevisions);
@@ -70,6 +72,51 @@ describeEmbeddedPostgres("activity service", () => {
     await tempDb?.cleanup();
   });
 
+  it("limits company activity lists", async () => {
+    const companyId = randomUUID();
+
+    await db.insert(companies).values({
+      id: companyId,
+      name: "Paperclip",
+      issuePrefix: `T${companyId.replace(/-/g, "").slice(0, 6).toUpperCase()}`,
+      requireBoardApprovalForNewAgents: false,
+    });
+
+    await db.insert(activityLog).values([
+      {
+        companyId,
+        actorType: "system",
+        actorId: "system",
+        action: "test.oldest",
+        entityType: "company",
+        entityId: companyId,
+        createdAt: new Date("2026-04-21T10:00:00.000Z"),
+      },
+      {
+        companyId,
+        actorType: "system",
+        actorId: "system",
+        action: "test.middle",
+        entityType: "company",
+        entityId: companyId,
+        createdAt: new Date("2026-04-21T11:00:00.000Z"),
+      },
+      {
+        companyId,
+        actorType: "system",
+        actorId: "system",
+        action: "test.newest",
+        entityType: "company",
+        entityId: companyId,
+        createdAt: new Date("2026-04-21T12:00:00.000Z"),
+      },
+    ]);
+
+    const result = await activityService(db).list({ companyId, limit: 2 });
+
+    expect(result.map((event) => event.action)).toEqual(["test.newest", "test.middle"]);
+  });
+
   it("returns compact usage and result summaries for issue runs", async () => {
     const companyId = randomUUID();
     const agentId = randomUUID();