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The above code looks correct - so not sure what the question is?

I want to use aws.apigatewayv2.API. But can't find an example similar to awsx.apigateway.API

How about this example: https://github.com/pulumi/examples/blob/master/aws-ts-apigatewayv2-http-api-quickcreate/index.ts

I am trying to do this. But it seems that it is not right. Is there an example where you can guide me to make several routes and keep them in a single endpoint?

// Copyright 2016-2019, Pulumi Corporation.  All rights reserved.

import * as aws from "@pulumi/aws";
import * as pulumi from "@pulumi/pulumi";
import { getName } from "./utils";

const stack = pulumi.getStack();
const project = pulumi.getProject();
const nameBucket = `${getName(project, stack)}`;
// Create the role for the Lambda to assume
const lambdaRole = new aws.iam.Role(`${nameBucket}-role`, {
  assumeRolePolicy: {
    Version: "2012-10-17",
    Statement: [
      {
        Action: "sts:AssumeRole",
        Principal: {
          Service: "<http://lambda.amazonaws.com|lambda.amazonaws.com>",
        },
        Effect: "Allow",
        Sid: "",
      },
    ],
  },
});
// Attach the fullaccess policy to the Lambda role created above
const rolepolicyattachment = new aws.iam.RolePolicyAttachment(
  `${nameBucket}-role-policy-attachment`,
  {
    role: lambdaRole,
    policyArn: aws.iam.ManagedPolicy.AWSLambdaBasicExecutionRole,
  }
);

// Create the namedUsersLambda to execute
const namedUsersLambda = new aws.lambda.Function(`${nameBucket}-namedUsers`, {
  code: new pulumi.asset.AssetArchive({
    ".": new pulumi.asset.FileArchive("./src/app/named-users"),
  }),
  runtime: "nodejs12.x",
  role: lambdaRole.arn,
  handler: "index.handler",
});
// Create the tagsLambda to execute
const tagsLambda = new aws.lambda.Function(`${nameBucket}-tags`, {
  code: new pulumi.asset.AssetArchive({
    ".": new pulumi.asset.FileArchive("./src/app/tags"),
  }),
  runtime: "nodejs12.x",
  role: lambdaRole.arn,
  handler: "index.handler",
});

// Give API Gateway lambdapermissionNamedUsers to invoke the Lambda
const lambdapermissionNamedUsers = new aws.lambda.Permission(
  `${nameBucket}-namedUsers`,
  {
    action: "lambda:InvokeFunction",
    principal: "<http://apigateway.amazonaws.com|apigateway.amazonaws.com>",
    function: namedUsersLambda,
  }
);
// Give API Gateway lambdapermissionTags to invoke the Lambda
const lambdapermissionTags = new aws.lambda.Permission(`${nameBucket}-tags`, {
  action: "lambda:InvokeFunction",
  principal: "<http://apigateway.amazonaws.com|apigateway.amazonaws.com>",
  function: tagsLambda,
});

// Set up the API Gateway
const apigwNamedUsers = new aws.apigatewayv2.Api(`${nameBucket}-namedUsers`, {
  protocolType: "HTTP",
  routeKey: "GET /named-users",
  target: namedUsersLambda.invokeArn,
});
// Set up the API Gateway
const apigwTags = new aws.apigatewayv2.Api(`${nameBucket}-tags`, {
  protocolType: "HTTP",
  routeKey: "GET /tags",
  target: tagsLambda.invokeArn,
});

export const endpointNamedUsers = apigwNamedUsers.apiEndpoint;
export const endpointTags = apigwTags.apiEndpoint;

Put an answer in #CJ909TL6P https://pulumi-community.slack.com/archives/CJ909TL6P/p1622855574044000?thread_ts=1622821601.043000&cid=CJ909TL6P You need an integration + route to attach routes to your API gateway v2