[codex] Harden issue recovery reliability (#4875)

## Thinking Path

> - Paperclip is the control plane for autonomous agent companies, so
non-terminal issue state must always have a clear live, waiting, or
recovery owner.
> - This change stays inside the server reliability and liveness
subsystem for assigned issue recovery, blocker attention, and live-run
polling.
> - Closed PR #4860 mixed this reliability work with separate
mutation-boundary policy changes, which made review and merge risk too
broad.
> - [PAP-2981](/PAP/issues/PAP-2981) asked for a replacement PR
containing only the remaining reliability slice and explicitly excluding
user-assignment and execution-policy restrictions.
> - Follow-up review also split `advanced` run-liveness continuation
behavior out of this PR so it can be reviewed separately.
> - The implementation hardens repeated recovery escalation, expands
blocker-attention coverage for explicit waiting and recovery paths, and
caps company live-run polling defaults.
> - The benefit is a smaller reliability PR that improves liveness
behavior without changing agent/user mutation authorization boundaries
or `advanced` continuation semantics.

## What Changed

- Avoid repeated liveness escalation updates when the source issue is
already blocked by the same open escalation.
- Treat open liveness escalation recovery issues, their source issues,
and their leaf blockers as covered waiting paths in blocker attention.
- Cap default company live-run polling at 50 rows for both `minCount`
and `limit`, including explicit zero values, to avoid unbounded
responses.
- Preserve the existing behavior where succeeded `advanced` runs are
considered productive/healthy for stranded-work recovery and are not
actionable bounded run-liveness continuations.
- Added focused server coverage for recovery dedupe, blocker attention,
liveness escalation, run continuations, and live-run polling.

## Verification

- `pnpm install --frozen-lockfile`
- `pnpm exec vitest run
server/src/__tests__/heartbeat-process-recovery.test.ts
server/src/__tests__/heartbeat-issue-liveness-escalation.test.ts
server/src/__tests__/issue-blocker-attention.test.ts
server/src/__tests__/run-continuations.test.ts
server/src/__tests__/agent-live-run-routes.test.ts`
- Result: 5 files passed, 63 tests passed.
- `pnpm --filter @paperclipai/server typecheck`
- Result: passed.
- No UI changes; screenshots are not applicable.

## Risks

- Recovery and blocker-attention classification changes can affect which
blocked chains are shown as covered versus needing attention.
- Live-run polling now treats omitted, invalid, or non-positive `limit`
/ `minCount` values as the capped default of 50.
- `advanced` run-liveness continuation behavior is intentionally
excluded from this PR and split for separate review.

> 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, code execution and GitHub CLI tool use, medium
reasoning effort.

## 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

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

server/src/routes/agents.ts

@@ -99,7 +99,8 @@ function readRunLogLimitBytes(value: unknown) {
 function readLiveRunsQueryInt(value: unknown, max: number, fallback = 0) {
   const parsed = Number(value);
   if (!Number.isFinite(parsed)) return fallback;
-  return Math.max(0, Math.min(max, Math.trunc(parsed)));
+  if (parsed <= 0) return fallback;
+  return Math.min(max, Math.trunc(parsed));
 }
 
 export function agentRoutes(
@@ -2821,8 +2822,8 @@ export function agentRoutes(
     const companyId = req.params.companyId as string;
     assertCompanyAccess(req, companyId);
 
-    const minCount = readLiveRunsQueryInt(req.query.minCount, 50);
-    const limit = readLiveRunsQueryInt(req.query.limit, 50);
+    const minCount = readLiveRunsQueryInt(req.query.minCount, 50, 50);
+    const limit = readLiveRunsQueryInt(req.query.limit, 50, 50);
 
     const columns = {
       id: heartbeatRuns.id,
@@ -2862,8 +2863,8 @@ export function agentRoutes(
       )
       .orderBy(desc(heartbeatRuns.createdAt));
 
-    const liveRuns = limit > 0 ? await liveRunsQuery.limit(limit) : await liveRunsQuery;
-    const targetRunCount = limit > 0 ? Math.min(minCount, limit) : minCount;
+    const liveRuns = await liveRunsQuery.limit(limit);
+    const targetRunCount = Math.min(minCount, limit);
 
     if (targetRunCount > 0 && liveRuns.length < targetRunCount) {
       const activeIds = liveRuns.map((r) => r.id);