feat(integration): prepaid billing, engine UI, credits console, direct tasks, v2 final

- Prepaid credit system: org wallet, debit on usage, chat gate, admin credit console
- Engine UI: /manager, /tasks, /tasks/[id], /workforce, /dashboard, /traces pages
- Direct task creation (HTTP POST /tasks, MCP tasks_create) at pending_manager_review
- Pause/resume/cancel/answer actions in engine API and UI
- Employee cap (7 per org default), review pipeline guard (active reviewer required)
- Scheduler: wide window prevents org starvation; archived employees excluded from cap
- Tenant isolation: project-id cross-org 404, engine never uses another tenant's sandbox
- Order route fix: manager built with pipeline states + employee profiles
- Contract extension: ModelGrantPort.get_org_policy with DefaultOrgPolicy
- Engine event types in @agy/contracts (task.step, task.gate, run.log, run.tool, team.changed)
- api-engine.ts typed client; api-credit.ts client
- Alembic migration c4d5e6f7a8b9: prepaid credit + engine UI tables
- 859 tests passed, 1 skipped; ruff/mypy/tsc/eslint/vitest all green

Refs: PLAN-v2.md §9 (T1–T43), todo-v2-final.md

apps/api/app/application/engine/state.py

@@ -19,6 +19,7 @@ truth, the status column is the summary existing APIs keep reading.
 
 from __future__ import annotations
 
+from app.application.engine.events import emit_task_step
 from app.core.errors import ConflictError, NotFoundError
 from app.domain.workforce.pipeline import (
     SIDE_STAGES,
@@ -46,14 +47,14 @@ async def advance(
 
     Raises ``ConflictError`` when the transition is illegal or when another
     worker moved the task first, and ``NotFoundError`` when the task has no
-    engine state row at all.
+    engine state row at all. A move that lands publishes one ``task.step``.
     """
     if not can_transition_stage(expected_from, to):
         raise ConflictError(
             f"گذار نابجا از {expected_from.value} به {to.value}."
         )
     try:
-        return await states.advance(task_id=task_id, expected_from=expected_from, to=to)
+        moved = await states.advance(task_id=task_id, expected_from=expected_from, to=to)
     except UnknownTaskError as exc:
         raise NotFoundError("این کار وضعیت موتور ندارد.") from exc
     except InvalidTransitionError as exc:
@@ -62,6 +63,15 @@ async def advance(
         raise ConflictError(
             "این کار هم‌اکنون توسط موتور دیگری در حرکت است؛ دوباره تلاش کنید."
         ) from exc
+    # The publisher never raises, so a broken bus cannot undo the move.
+    await emit_task_step(
+        task_id=moved.task_id,
+        organization_id=moved.organization_id,
+        from_stage=expected_from,
+        to_stage=to,
+        pipeline=moved.pipeline,
+    )
+    return moved
 
 
 async def park_dependents(