Pulumi FSharp code to create an API gateway entry for a lambda function that's hosting Asp.net core (eg in giraffe)

PulumiFragment.fs

    let infra () =
    
        ...
    
        let openApiSpec (name, arn) =
            let quotedTitle = "\"" + name + "api\""
            let quotedUri   = sprintf "\"arn:aws:apigateway:%s:lambda:path/2015-03-31/functions/%s/invocations\"" Pulumi.Aws.Config.Region arn
            """{
  "openapi": "3.0.1",
  "info": {
    "title": """ + quotedTitle + """,
    "version": "1.0"
  },
  "paths": {
    "/{proxy+}": {
      "x-amazon-apigateway-any-method": {
        "x-amazon-apigateway-integration": {
          "uri": """ + quotedUri + """,
          "passthroughBehavior": "when_no_match",
          "httpMethod": "POST",
          "type": "aws_proxy"
        }
      }
    },
    "/": {
      "x-amazon-apigateway-any-method": {
        "x-amazon-apigateway-integration": {
          "uri": """ + quotedUri + """,
          "passthroughBehavior": "when_no_match",
          "httpMethod": "POST",
          "type": "aws_proxy"
        }
      }
    }
  },
  "components": {}
}"""

        let restApiArgs lambdaName lambdaArn =
            let openApiSpec =
                Outputs.pair lambdaName lambdaArn
                |> Outputs.apply openApiSpec

            RestApiArgs(Body = io openApiSpec)

        let restApi     = RestApi("websiteApi", (restApiArgs websiteLambda.Name websiteLambda.Arn))
        let deployment  = Deployment("websiteApiDeployment", DeploymentArgs(RestApi = io restApi.Id, StageName = input ""))
        let prodStage   = Stage("websiteApiProd", StageArgs(RestApi = io restApi.Id,  Deployment = io deployment.Id, StageName = input "Prod"))