feat(backend): Add Celery worker infrastructure with task stubs

- Add Celery app configuration with Redis broker/backend
- Add task modules: agent, workflow, cost, git, sync
- Add task stubs for:
  - Agent execution (spawn, heartbeat, terminate)
  - Workflow orchestration (start sprint, checkpoint, code review)
  - Cost tracking (record usage, calculate, generate report)
  - Git operations (clone, commit, push, sync)
  - External sync (import issues, export updates)
- Add task tests directory structure
- Configure for production-ready Celery setup

Implements #18

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/celery_app.py

@@ -0,0 +1,110 @@
+# app/celery_app.py
+"""
+Celery application configuration for Syndarix.
+
+This module configures the Celery app for background task processing:
+- Agent execution tasks (LLM calls, tool execution)
+- Git operations (clone, commit, push, PR creation)
+- Issue synchronization with external trackers
+- Workflow state management
+- Cost tracking and budget monitoring
+
+Architecture:
+- Redis as message broker and result backend
+- Queue routing for task isolation
+- JSON serialization for cross-language compatibility
+- Beat scheduler for periodic tasks
+"""
+
+from celery import Celery
+
+from app.core.config import settings
+
+# Create Celery application instance
+celery_app = Celery(
+    "syndarix",
+    broker=settings.celery_broker_url,
+    backend=settings.celery_result_backend,
+)
+
+# Define task queues with their own exchanges and routing keys
+TASK_QUEUES = {
+    "agent": {"exchange": "agent", "routing_key": "agent"},
+    "git": {"exchange": "git", "routing_key": "git"},
+    "sync": {"exchange": "sync", "routing_key": "sync"},
+    "default": {"exchange": "default", "routing_key": "default"},
+}
+
+# Configure Celery
+celery_app.conf.update(
+    # Serialization
+    task_serializer="json",
+    accept_content=["json"],
+    result_serializer="json",
+    # Timezone
+    timezone="UTC",
+    enable_utc=True,
+    # Task imports for auto-discovery
+    imports=("app.tasks",),
+    # Default queue
+    task_default_queue="default",
+    # Task queues configuration
+    task_queues=TASK_QUEUES,
+    # Task routing - route tasks to appropriate queues
+    task_routes={
+        "app.tasks.agent.*": {"queue": "agent"},
+        "app.tasks.git.*": {"queue": "git"},
+        "app.tasks.sync.*": {"queue": "sync"},
+        "app.tasks.*": {"queue": "default"},
+    },
+    # Time limits per ADR-003
+    task_soft_time_limit=300,  # 5 minutes soft limit
+    task_time_limit=600,  # 10 minutes hard limit
+    # Result expiration - 24 hours
+    result_expires=86400,
+    # Broker connection retry
+    broker_connection_retry_on_startup=True,
+    # Beat schedule for periodic tasks
+    beat_schedule={
+        # Cost aggregation every hour per ADR-012
+        "aggregate-daily-costs": {
+            "task": "app.tasks.cost.aggregate_daily_costs",
+            "schedule": 3600.0,  # 1 hour in seconds
+        },
+        # Reset daily budget counters at midnight UTC
+        "reset-daily-budget-counters": {
+            "task": "app.tasks.cost.reset_daily_budget_counters",
+            "schedule": 86400.0,  # 24 hours in seconds
+        },
+        # Check for stale workflows every 5 minutes
+        "recover-stale-workflows": {
+            "task": "app.tasks.workflow.recover_stale_workflows",
+            "schedule": 300.0,  # 5 minutes in seconds
+        },
+        # Incremental issue sync every minute per ADR-011
+        "sync-issues-incremental": {
+            "task": "app.tasks.sync.sync_issues_incremental",
+            "schedule": 60.0,  # 1 minute in seconds
+        },
+        # Full issue reconciliation every 15 minutes per ADR-011
+        "sync-issues-full": {
+            "task": "app.tasks.sync.sync_issues_full",
+            "schedule": 900.0,  # 15 minutes in seconds
+        },
+    },
+    # Task execution settings
+    task_acks_late=True,  # Acknowledge tasks after execution
+    task_reject_on_worker_lost=True,  # Reject tasks if worker dies
+    worker_prefetch_multiplier=1,  # Fair task distribution
+)
+
+# Auto-discover tasks from task modules
+celery_app.autodiscover_tasks(
+    [
+        "app.tasks.agent",
+        "app.tasks.git",
+        "app.tasks.sync",
+        "app.tasks.workflow",
+        "app.tasks.cost",
+    ]
+)