feat: realtime WebSocket layer for live events and streaming logs

- Backend: ConnectionManager, Redis-backed bus with in-process fallback,
  channel authorization, and typed emit helpers wired into workers
  (ai_runtime, sandbox_gateway), workforce/sandbox/billing/audit/error services.
- Frontend: single shared WS client with backoff + heartbeat, RealtimeProvider,
  useLiveChannel/useLiveEvent hooks, live indicators on task detail, manager
  chat, dashboard, traces, sandbox terminal, admin errors, and billing.
- Contracts: WsEvent/WsServerFrame/WsClientFrame types mirroring the port.

All 255 backend tests pass; web typecheck and build pass.

apps/api/app/application/services/billing_service.py

@@ -14,6 +14,7 @@ from __future__ import annotations
 from datetime import datetime
 
 from app.application.ports import PaymentProviderPort
+from app.application.ports.realtime import emit_wallet_changed
 from app.core.errors import NotFoundError, PermissionDeniedError, ValidationError
 from app.domain.billing.models import (
     CreditWallet,
@@ -121,6 +122,11 @@ class BillingService:
             # Refuse to leave a wallet in debt; undo and surface the conflict.
             await self.wallets.adjust(organization_id=organization_id, delta=-amount)
             raise ValidationError("اعتبار کافی برای این کسر وجود ندارد.")
+        # Live push: the sidebar credit badge and the billing page follow the
+        # wallet as it moves, whoever moved it.
+        await emit_wallet_changed(
+            organization_id=organization_id, balance=wallet.balance
+        )
         return wallet
 
     async def start_checkout(
@@ -177,8 +183,13 @@ class BillingService:
             return payment
 
         if succeeded:
-            await self.wallets.adjust(organization_id=organization_id, delta=payment.amount)
+            wallet = await self.wallets.adjust(
+                organization_id=organization_id, delta=payment.amount
+            )
             final = await self.payments.set_status(payment_id, PaymentStatus.SUCCEEDED)
+            await emit_wallet_changed(
+                organization_id=organization_id, balance=wallet.balance
+            )
         else:
             final = await self.payments.set_status(payment_id, PaymentStatus.FAILED)
         return final or payment