feat: setup FastAPI main app with routers and test fixtures

- Main FastAPI app with all routers included
- CORS middleware for frontend
- Test fixtures with in-memory SQLite database
- Placeholder routers for future tasks

backend/tests/conftest.py

@@ -0,0 +1,32 @@
+import pytest
+import pytest_asyncio
+from sqlalchemy.ext.asyncio import create_async_engine, AsyncSession, async_sessionmaker
+from app.database import Base, get_db
+from app.main import app
+from httpx import AsyncClient
+
+TEST_DATABASE_URL = "sqlite+aiosqlite:///./test.db"
+
+@pytest_asyncio.fixture
+async def db():
+    engine = create_async_engine(TEST_DATABASE_URL, echo=False)
+    async with engine.begin() as conn:
+        await conn.run_sync(Base.metadata.create_all)
+    
+    async_session = async_sessionmaker(engine, class_=AsyncSession, expire_on_commit=False)
+    async with async_session() as session:
+        yield session
+    
+    async with engine.begin() as conn:
+        await conn.run_sync(Base.metadata.drop_all)
+    await engine.dispose()
+
+@pytest_asyncio.fixture
+async def client(db):
+    async def override_get_db():
+        yield db
+    
+    app.dependency_overrides[get_db] = override_get_db
+    async with AsyncClient(app=app, base_url="http://test") as ac:
+        yield ac
+    app.dependency_overrides.clear()