I have an OpenAPI spec for an api which I am deploying via CDK. The spec looks like:
openapi: 3.0.1
info:
  title: My API
  description: My REST API with CORS enabled
  version: 0.1.0
x-amazon-apigateway-cors:
  allowOrigins:
    - "*"
  allowCredentials: true
  exposeHeaders:
    - "x-apigateway-header"
    - "x-amz-date"
    - "content-type"
  maxAge: 3600
  allowMethods:
    - "*"
  allowHeaders":
    - "x-apigateway-header"
    - "x-amz-date"
    - "content-type"
    - "Authorization"
components:
  securitySchemes:
    lambda:
      type: "apiKey"
      name: "Authorization"
      in: "header"
      x-amazon-apigateway-authtype: "custom"
      x-amazon-apigateway-authorizer:
        authorizerUri: "{{my-lambda-authorizer}}"
        authorizerResultTtlInSeconds: 300
        type: "token" 
paths:
  /user/{id}:
    get:
      summary: Get info of specified user.
      parameters:
        - in: path
          name: id
          required: true
          schema:
            type: string
      responses:
        '200':
          description: OK
          content:
            application/json:
              schema:
                $ref: '#/components/schemas/User'
      security:
        - lambda: []
      x-amazon-apigateway-integration:
        uri: "{{my-lambda}}"
        passthroughBehavior: "when_no_match"
        httpMethod: "POST"
        type: "aws_proxy"
When I try to access this via fetch(), I get an error Failed to load resource: Origin http://localhost:8000 is not allowed by Access-Control-Allow-Origin.
fetch('https://api.example.com/user/1')
        .then(response => response.json())
        .then((user: User) => {
            // do something
        })
        .catch((err) => {
            console.log("Error: " + err);
        });
The API is accessible at api.example.com and I am running the website locally using Gatsby at localhost:8000.
The AWS docs seem to state that CORS is enabled when I put x-amazon-apigateway-cors at the root of the spec, but CORS doesn't seem to be enabled (or working) when I try to access the API.  How do I enable CORS for my API without needing to configure it in the console?
 
    