Dispatch assigned todo work during recovery sweeps (#4614)

## Thinking Path

> - Paperclip orchestrates AI agents for autonomous companies.
> - Agent assignments must reliably turn into heartbeat work without
board operators manually nudging stuck tasks.
> - The stranded-assignment recovery sweep already handles failed or
lost runs.
> - But assigned `todo` issues with no prior run could sit idle because
there was nothing to retry or recover.
> - This pull request dispatches those never-started assigned todos as
normal assignment wakes.
> - The benefit is that recovery fixes missed initial dispatches without
creating unnecessary recovery issues.

## What Changed

- Added an initial assigned-todo dispatch path to the recovery service
when an assigned `todo` issue has no heartbeat run yet.
- Reused invocation budget hard-stop checks before dispatching or
requeueing recovery work.
- Counted `assignmentDispatched` in startup/scheduled recovery logs.
- Added heartbeat recovery regressions for first dispatch, duplicate
queued wake prevention, budget-blocked skips, and paused-agent skips.

## Verification

- `pnpm exec vitest run
server/src/__tests__/heartbeat-process-recovery.test.ts`

## Risks

- Low to medium risk: this changes liveness recovery behavior for
assigned `todo` issues, but it stays on the existing assignment wake
path and skips paused or budget-blocked agents.
- No migrations.

> 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 coding agent based on GPT-5, tool-enabled local
repository and shell access, Paperclip heartbeat context.

## 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

server/src/services/recovery/service.ts

@@ -343,6 +343,21 @@ export function recoveryService(db: Db, deps: { enqueueWakeup: RecoveryWakeup })
     return Boolean(run || deferredWake);
   }
 
+  async function hasQueuedIssueWake(companyId: string, issueId: string) {
+    return db
+      .select({ id: agentWakeupRequests.id })
+      .from(agentWakeupRequests)
+      .where(
+        and(
+          eq(agentWakeupRequests.companyId, companyId),
+          eq(agentWakeupRequests.status, "queued"),
+          sql`${agentWakeupRequests.payload} ->> 'issueId' = ${issueId}`,
+        ),
+      )
+      .limit(1)
+      .then((rows) => Boolean(rows[0]));
+  }
+
   async function enqueueStrandedIssueRecovery(input: {
     issueId: string;
     agentId: string;
@@ -386,6 +401,34 @@ export function recoveryService(db: Db, deps: { enqueueWakeup: RecoveryWakeup })
     return queued;
   }
 
+  async function enqueueInitialAssignedTodoDispatch(issue: typeof issues.$inferSelect, agentId: string) {
+    return deps.enqueueWakeup(agentId, {
+      source: "assignment",
+      triggerDetail: "system",
+      reason: "issue_assigned",
+      payload: {
+        issueId: issue.id,
+        mutation: "assigned_todo_liveness_dispatch",
+      },
+      requestedByActorType: "system",
+      requestedByActorId: null,
+      contextSnapshot: {
+        issueId: issue.id,
+        taskId: issue.id,
+        wakeReason: "issue_assigned",
+        source: "issue.assigned_todo_liveness_dispatch",
+      },
+    });
+  }
+
+  async function isInvocationBudgetBlocked(issue: typeof issues.$inferSelect, agentId: string) {
+    const budgetBlock = await budgets.getInvocationBlock(issue.companyId, agentId, {
+      issueId: issue.id,
+      projectId: issue.projectId,
+    });
+    return Boolean(budgetBlock);
+  }
+
   async function reconcileUnassignedBlockingIssues() {
     const candidates = await db
       .select({
@@ -1526,6 +1569,7 @@ export function recoveryService(db: Db, deps: { enqueueWakeup: RecoveryWakeup })
       );
 
     const result = {
+      assignmentDispatched: 0,
       dispatchRequeued: 0,
       continuationRequeued: 0,
       orphanBlockersAssigned: 0,
@@ -1574,7 +1618,28 @@ export function recoveryService(db: Db, deps: { enqueueWakeup: RecoveryWakeup })
       }
 
       if (issue.status === "todo") {
-        if (!latestRun || latestRun.status === "succeeded") {
+        if (!latestRun) {
+          if (await hasQueuedIssueWake(issue.companyId, issue.id)) {
+            result.skipped += 1;
+            continue;
+          }
+
+          if (await isInvocationBudgetBlocked(issue, agentId)) {
+            result.skipped += 1;
+            continue;
+          }
+
+          const queued = await enqueueInitialAssignedTodoDispatch(issue, agentId);
+          if (queued) {
+            result.assignmentDispatched += 1;
+            result.issueIds.push(issue.id);
+          } else {
+            result.skipped += 1;
+          }
+          continue;
+        }
+
+        if (latestRun.status === "succeeded") {
           result.skipped += 1;
           continue;
         }
@@ -1599,6 +1664,11 @@ export function recoveryService(db: Db, deps: { enqueueWakeup: RecoveryWakeup })
           continue;
         }
 
+        if (await isInvocationBudgetBlocked(issue, agentId)) {
+          result.skipped += 1;
+          continue;
+        }
+
         const queued = await enqueueStrandedIssueRecovery({
           issueId: issue.id,
           agentId,
@@ -1640,6 +1710,11 @@ export function recoveryService(db: Db, deps: { enqueueWakeup: RecoveryWakeup })
         continue;
       }
 
+      if (await isInvocationBudgetBlocked(issue, agentId)) {
+        result.skipped += 1;
+        continue;
+      }
+
       const queued = await enqueueStrandedIssueRecovery({
         issueId: issue.id,
         agentId,