使用Serverless Framework部署FastAPI到AWS Lambda时遇内部服务器错误：无法导入FastAPI

我用Serverless Framework把FastAPI部署到了AWS Lambda，本地测试Lambda函数完全正常，但部署后访问URL时浏览器返回“Internal Server Error”（500）。

查看日志后发现以下错误：

[ERROR] Runtime.ImportModuleError: Unable to import module 'handler': No module named 'fastapi'
Traceback (most recent call last):
INIT_REPORT Init Duration: 99.52 ms     Phase: init     Status: error   Error Type: Runtime.ImportModuleError

handler.py #

from fastapi import FastAPI
from mangum import Mangum

app = FastAPI()

@app.get("/")
def read_root():
    return {"message": "Hello, this is Daksh from FastAPI on AWS Lambda!"}

handler = Mangum(app)

serverless.yml #

org: daksh
service: fastapi-lambda

provider:
  name: aws
  runtime: python3.10
  region: ap-northeast-1
  deploymentBucket:
    name: fastapi-lambda-deployments-347775769886

functions:
  app:
    handler: handler.handler
    events:
      - http:
          path: /{proxy+}  
          method: any
    memorySize: 128 
    timeout: 10  
    environment:
      PYTHONPATH: "/var/runtime:/var/task"

package:
  exclude:
    - node_modules/**
    - env/**
    - .serverless/**

plugins:
  - serverless-python-requirements

custom:
  pythonRequirements:
    dockerizePip: non-linux
    layer: 
      path: requirements.txt
      name: fastapi-serverless-lambda
      compatibility: python3.10

requirements.txt #

fastapi==0.115.6
mangum==0.19.0
# other packages

我已经做了这些尝试：

• 用Serverless Framework本地运行Lambda函数没有问题
• 函数部署成功，但日志里出现Runtime.ImportModuleError，提示找不到fastapi
• 我在用serverless-python-requirements插件处理依赖

请问这个错误的原因是什么？我该怎么解决才能让FastAPI在AWS Lambda上正常运行？

备注：内容来源于stack exchange，提问作者Godhani Daksh