[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

packages/shared/src/constants.ts

@@ -67,9 +67,7 @@ export const AGENT_ROLE_LABELS: Record<AgentRole, string> = {
 };
 
 export const AGENT_DEFAULT_MAX_CONCURRENT_RUNS = 5;
-
 export const WORKSPACE_BRANCH_ROUTINE_VARIABLE = "workspaceBranch";
-
 export const AGENT_ICON_NAMES = [
   "bot",
   "cpu",
@@ -353,6 +351,7 @@ export type WakeupRequestStatus = (typeof WAKEUP_REQUEST_STATUSES)[number];
 
 export const HEARTBEAT_RUN_STATUSES = [
   "queued",
+  "scheduled_retry",
   "running",
   "succeeded",
   "failed",

packages/shared/src/types/heartbeat.ts

@@ -39,6 +39,10 @@ export interface HeartbeatRun {
   processStartedAt: Date | null;
   retryOfRunId: string | null;
   processLossRetryCount: number;
+  scheduledRetryAt?: Date | null;
+  scheduledRetryAttempt?: number;
+  scheduledRetryReason?: string | null;
+  retryExhaustedReason?: string | null;
   livenessState: RunLivenessState | null;
   livenessReason: string | null;
   continuationAttempt: number;

packages/shared/src/types/issue.ts

@@ -217,6 +217,7 @@ export interface Issue {
   originKind?: IssueOriginKind;
   originId?: string | null;
   originRunId?: string | null;
+  originFingerprint?: string | null;
   requestDepth: number;
   billingCode: string | null;
   assigneeAdapterOverrides: IssueAssigneeAdapterOverrides | null;

packages/shared/src/types/routine.ts

@@ -95,6 +95,7 @@ export interface RoutineRun {
   triggeredAt: Date;
   idempotencyKey: string | null;
   triggerPayload: Record<string, unknown> | null;
+  dispatchFingerprint: string | null;
   linkedIssueId: string | null;
   coalescedIntoRunId: string | null;
   failureReason: string | null;