[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

ui/src/api/activity.ts

@@ -15,6 +15,11 @@ export interface RunForIssue {
   usageJson: Record<string, unknown> | null;
   resultJson: Record<string, unknown> | null;
   logBytes?: number | null;
+  retryOfRunId?: string | null;
+  scheduledRetryAt?: string | null;
+  scheduledRetryAttempt?: number;
+  scheduledRetryReason?: string | null;
+  retryExhaustedReason?: string | null;
   livenessState?: RunLivenessState | null;
   livenessReason?: string | null;
   continuationAttempt?: number;
@@ -31,11 +36,12 @@ export interface IssueForRun {
 }
 
 export const activityApi = {
-  list: (companyId: string, filters?: { entityType?: string; entityId?: string; agentId?: string }) => {
+  list: (companyId: string, filters?: { entityType?: string; entityId?: string; agentId?: string; limit?: number }) => {
     const params = new URLSearchParams();
     if (filters?.entityType) params.set("entityType", filters.entityType);
     if (filters?.entityId) params.set("entityId", filters.entityId);
     if (filters?.agentId) params.set("agentId", filters.agentId);
+    if (filters?.limit) params.set("limit", String(filters.limit));
     const qs = params.toString();
     return api.get<ActivityEvent[]>(`/companies/${companyId}/activity${qs ? `?${qs}` : ""}`);
   },