The S3 API reference [1] is closest to a formal spec there is. The request, response and the error codes are pretty well documented.
[1]: https://docs.aws.amazon.com/AmazonS3/latest/API/API_Operatio...
[1]: https://docs.aws.amazon.com/AmazonS3/latest/API/API_Operatio...
I searched on that page and didn't find anything but I've seen it mentioned elsewhere that they are catered for but I haven't found any documentation for that.
I'm particularly interested in the temporary ones - 302, 303 and 307.