feat(backend): add API routes

backend/src/api/routes/stats.py

@@ -0,0 +1,26 @@
+from collections.abc import AsyncGenerator
+from typing import Annotated
+
+from fastapi import APIRouter, Depends
+from sqlalchemy.ext.asyncio import AsyncSession
+
+from src.db.database import get_db
+from src.schemas import StatsResponse
+from src.services import StatsService
+
+router = APIRouter()
+
+
+async def get_stats_service(
+    db: Annotated[AsyncSession, Depends(get_db)],
+) -> AsyncGenerator[StatsService, None]:
+    """Dependency for StatsService."""
+    yield StatsService(db)
+
+
+@router.get("", response_model=StatsResponse)
+async def get_stats(
+    service: Annotated[StatsService, Depends(get_stats_service)],
+) -> StatsResponse:
+    """Get question counts by difficulty, category, and pattern."""
+    return await service.get_stats()