I found there's a newer solution provided by awslabs which does more or less the same as this, using a different approach:
https://github.com/awslabs/aws-lambda-web-adapter

The core difference to this library is that the above builds the adapter as a lambda layer and forwards the request to http server (your application) running on the same instance.

It supports LambdaFunctionURL by design and works with any http server (regardless of the programming language used).

You might also use my own library, which uses the same approach as this one: https://github.com/its-felix/aws-lambda-go-http-adapter/tree/main
(though I myself only use it for hobby projects, for any work related things I recommend staying with the aws provided solutions)