Documentation states you can access APIs with wildcard allow origin but it's not the case at least with AWS API Gateway

I have Lambda which uses API Gateway’s http-api, I have configured CORS as below…

httpApi:
    cors:
      allowedOrigins: "*"
      allowedMethods: "*"
      allowedHeaders: "*"
      allowCredentials: false

I have set my response headers…

return {
        statusCode: 201,
        body: JSON.stringify({
            publicKey: 'publicKey',
            privateKey: 'privateKey',
        }),
        headers: {
            'Content-Type': 'application/json',
            'Access-Control-Allow-Origin': '*',
        },
    };

and yet i still get CORS errors when making the request from the Figma plugin.

The request works if set Origin: null within Postman, so to me it seems that the only solution here is to use a Proxy which I am not keen to do.

Is this a specific issue with API Gateway?