How to update Request's session in a FastAPI middleware?

I want to change request.session in middleware. But it doesn't change.

@app.middleware("http")
async def renewal_token(request: Request, call_next):
    response = await call_next(request)
    now = datetime.now()
    expire = now + timedelta(minutes=30)
    session_id = request.session["session_id"]
    request.session["token_expiry"] = expire.timestamp()  # My problem
    response.set_cookie(key="Authorization", value=session_id, expires=expire.replace(tzinfo=timezone.utc))
    return response

I cleared request.session but it still doesn't work.

...
request.session.clear()
request.session["token_expiry"] = expire.timestamp()
...