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/index.ts

@@ -682,6 +682,7 @@ export async function startServer(): Promise<StartedServer> {
         const reconciled = await heartbeat.reconcileStrandedAssignedIssues();
         if (
           promotion.promoted > 0 ||
+          reconciled.assignmentDispatched > 0 ||
           reconciled.dispatchRequeued > 0 ||
           reconciled.continuationRequeued > 0 ||
           reconciled.escalated > 0
@@ -740,6 +741,7 @@ export async function startServer(): Promise<StartedServer> {
           const reconciled = await heartbeat.reconcileStrandedAssignedIssues();
           if (
             promotion.promoted > 0 ||
+            reconciled.assignmentDispatched > 0 ||
             reconciled.dispatchRequeued > 0 ||
             reconciled.continuationRequeued > 0 ||
             reconciled.escalated > 0