Initial commit: Backend API Phase 1a complete

- FastAPI backend with JWT auth
- PostgreSQL database schema
- Trees and Sessions CRUD APIs
- Export functionality (Markdown, Text, HTML)
- Docker setup for local development
- Alembic migrations

backend/app/core/database.py

@@ -0,0 +1,37 @@
+from sqlalchemy.ext.asyncio import AsyncSession, create_async_engine, async_sessionmaker
+from sqlalchemy.orm import DeclarativeBase
+from .config import settings
+
+# Create async engine
+engine = create_async_engine(
+    settings.DATABASE_URL,
+    echo=settings.DEBUG,
+    future=True
+)
+
+# Create async session factory
+async_session_maker = async_sessionmaker(
+    engine,
+    class_=AsyncSession,
+    expire_on_commit=False
+)
+
+
+class Base(DeclarativeBase):
+    """Base class for all database models."""
+    pass
+
+
+async def get_db() -> AsyncSession:
+    """Dependency to get database session."""
+    async with async_session_maker() as session:
+        try:
+            yield session
+        finally:
+            await session.close()
+
+
+async def init_db():
+    """Initialize database tables."""
+    async with engine.begin() as conn:
+        await conn.run_sync(Base.metadata.create_all)