GraphQL Mesh not working on AWS Lambda

[mr-nagashima]

I created the Lambda function (index.ts) below with reference to "https://the-guild.dev/graphql/mesh/docs/getting-started/deploy-mesh-gateway#deploy-mesh-on-aws-lambda".
Before processing the above URL, we obtain the environment variables of the backend endpoint, issue an HTTP request directly to the backend, and confirm that the API can be called.

index.ts

// https://the-guild.dev/graphql/mesh/docs/getting-started/deploy-mesh-gateway#deploy-mesh-on-aws-lambda
//
import { APIGatewayEvent, APIGatewayProxyResult, Context } from "aws-lambda";
import type { Handler } from "@aws-cdk/aws-lambda";
import { createBuiltMeshHTTPHandler } from "./.mesh";
// for debug
import dotenv from "dotenv";
import axios, { AxiosRequestConfig, AxiosResponse, AxiosError } from "axios";

interface ServerContext {
  event: APIGatewayEvent;
  lambdaContext: Context;
}

const meshHTTP = createBuiltMeshHTTPHandler<ServerContext>();

export async function handler(
  event: APIGatewayEvent,
  lambdaContext: Context
): Promise<APIGatewayProxyResult> {
  const url = new URL(event.path, "http://0.0.0.0");

  dotenv.config();

  if (process.env.LAMBDA_DEBUG != null) {
    console.log(`BACKEND_ENDPOINT: ${process.env.BACKEND_ENDPOINT}`);
    console.log(`LAMBDA_DEBUG: ${process.env.LAMBDA_DEBUG}`);

    // for debug (Check communication with backend)
    const options: AxiosRequestConfig = {
      url: `http://${process.env.BACKEND_ENDPOINT}/company.v1.CompanyService/ListCompanies`,
      method: "POST",
      headers: {
        "Content-Type": "application/json",
      },
      data: {},
    };
    try {
      const response: AxiosResponse = await axios(options);
      console.log(`Response from backend: ${JSON.stringify(response.data)}`);
    } catch (error) {
      console.error(`Error from backend: ${JSON.stringify(error)}`);
    }

    console.log(`Event: ${JSON.stringify(event, null, 2)}`);
  }

  if (event.queryStringParameters != null) {
    // for debug
    console.log(
      `Event.queryStringParameters: ${JSON.stringify(
        event.queryStringParameters,
        null,
        2
      )}`
    );

    for (const name in event.queryStringParameters) {
      const value = event.queryStringParameters[name];
      if (value != null) {
        url.searchParams.set(name, value);
      }
    }
  }

  const response = await meshHTTP.fetch(
    url,
    {
      // For v1.0 you should use event.httpMethod
      method: event.requestContext.http.method,
      headers: event.headers as HeadersInit,
      body: event.body
        ? Buffer.from(event.body, event.isBase64Encoded ? "base64" : "utf8")
        : undefined,
    },
    {
      event,
      lambdaContext,
    }
  );

  // for debug
  if (process.env.LAMBDA_DEBUG != null) {
    console.log("%o", meshHTTP);
  }

  console.log(`Response: ${JSON.stringify(response, null, 2)}`);

  const responseHeaders: Record<string, string> = Object.fromEntries(
    response.headers.entries()
  );

  return {
    statusCode: response.status,
    headers: responseHeaders,
    body: await response.text(),
    isBase64Encoded: false,
  };
}

.meshrc.yaml is as follows.
Endpoint is set as an environment variable.

.meshrc.yaml

sources:
  - name: billing_account
    handler:
      grpc:
        endpoint: "{env.BACKEND_ENDPOINT}"
        source: ./proto/billing_account/v1/billing_account.proto
  - name: company
    handler:
      grpc:
        endpoint: "{env.BACKEND_ENDPOINT}"
        source: ./proto/company/v1/company.proto
    :

If you access it in the same way as in the local environment (npm run dev), you will get 404 as below.

Response: 
{
    "bodyInit": null,
    "options": {
        "status": 404,
        "statusText": "Not Found"
    },
    "bodyUsed": false,
    "contentType": null,
    "contentLength": null,
    "_generatedBody": null,
    "headers": {
        "objectNormalizedKeysOfHeadersInit": [],
        "objectOriginalKeysOfHeadersInit": [],
        "_setCookies": []
    },
    "status": 404,
    "statusText": "Not Found",
    "url": "",
    "redirected": false,
    "type": "default"
}

What is this 404 for?
(I tried to remove M's environment variables and write it directly, but the result was the same.)

Please let me know if there is anything wrong with my method.
Thank you for your advice.