[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/services/dashboard.ts

@@ -10,6 +10,10 @@ function formatUtcDateKey(date: Date): string {
   return date.toISOString().slice(0, 10);
 }
 
+export function getUtcMonthStart(date: Date): Date {
+  return new Date(Date.UTC(date.getUTCFullYear(), date.getUTCMonth(), 1));
+}
+
 function getRecentUtcDateKeys(now: Date, days: number): string[] {
   const todayUtc = Date.UTC(now.getUTCFullYear(), now.getUTCMonth(), now.getUTCDate());
   return Array.from({ length: days }, (_, index) => {
@@ -76,7 +80,7 @@ export function dashboardService(db: Db) {
       }
 
       const now = new Date();
-      const monthStart = new Date(Date.UTC(now.getUTCFullYear(), now.getUTCMonth(), 1));
+      const monthStart = getUtcMonthStart(now);
       const runActivityDays = getRecentUtcDateKeys(now, DASHBOARD_RUN_ACTIVITY_DAYS);
       const runActivityStart = new Date(`${runActivityDays[0]}T00:00:00.000Z`);
       const [{ monthSpend }] = await db