show me how to create an apigatewayv2 REST API and set the default route

Sure, here is a simple Pulumi program written in TypeScript that demonstrates how to create an API Gateway Version 2 and set the $default route. This example uses the aws.apigatewayv2.Api and aws.apigatewayv2.Route resources.

This program creates an HTTP API Gateway and a default route. This route would forward all requests to an HTTP integration, which could be your application load balancer, another HTTP endpoint, a Lambda function, and so on. In this program, we are simply making a mock integration.

Here's the TypeScript code:

import * as pulumi from "@pulumi/pulumi";
import * as aws from "@pulumi/aws";


// Create an API
let myApi = new aws.apigatewayv2.Api("myApi", {
    protocolType: "HTTP",
    target: "https://example.com", // a mock target
});

// Create a route
let defaultRoute = new aws.apigatewayv2.Route("defaultRoute", {
    apiId: myApi.id,
    routeKey: "$default",
    target: "integrations/000000",
});

// Export the URL of the API
export const url = myApi.apiEndpoint;

Here's what the code does:

The aws.apigatewayv2.Api instance myApi represents your HTTP API. The target property is an HTTP endpoint that the API will proxy. Note that in this example, the HTTP API does not integrate with a real target; it simply points to a placeholder URL. You'd replace https://example.com with the URL of your own backend service.
The aws.apigatewayv2.Route instance defaultRoute represents a route associated with your API. The routeKey property is set to $default, which means this route will match any request that is not matched by other routes.
We use a target of the form integrations/000000 - a mock integration, as a stand-in for your actual integration. In a real application, this could e.g., refer to a Lambda function ("integrations/${myLambdaIntegration.id}") or refer to an HTTP endpoint ("integrations/${myHttpIntegration.id}").

For more details:

Check Pulumi Registry for aws.apigatewayv2.Api
Check Pulumi Registry for aws.apigatewayv2.Route