How do you integrate an async SQLAlchemy database with FastAPI?

# pip install sqlalchemy asyncpg
from sqlalchemy.ext.asyncio import create_async_engine, AsyncSession, async_sessionmaker
from sqlalchemy.orm import DeclarativeBase, Mapped, mapped_column
from sqlalchemy import select
from fastapi import FastAPI, Depends
from typing import Annotated

DATABASE_URL = "postgresql+asyncpg://user:pass@localhost/db"

engine = create_async_engine(DATABASE_URL, echo=True)
AsyncSessionLocal = async_sessionmaker(engine, expire_on_commit=False)

class Base(DeclarativeBase):
    pass

class User(Base):
    __tablename__ = "users"
    id:       Mapped[int] = mapped_column(primary_key=True)
    username: Mapped[str] = mapped_column(unique=True)
    email:    Mapped[str]

# DB dependency — yields session, always closes it
async def get_db() -> AsyncSession:
    async with AsyncSessionLocal() as session:
        yield session

DBDep = Annotated[AsyncSession, Depends(get_db)]

app = FastAPI()

@app.on_event("startup")
async def startup():
    async with engine.begin() as conn:
        await conn.run_sync(Base.metadata.create_all)  # create tables

@app.get("/users")
async def list_users(db: DBDep):
    result = await db.execute(select(User))
    users = result.scalars().all()
    return users

@app.post("/users", status_code=201)
async def create_user(username: str, email: str, db: DBDep):
    user = User(username=username, email=email)
    db.add(user)
    await db.commit()
    await db.refresh(user)
    return user