Aurora is absolutely a fork of MySQL; they're careful never to explicitly admit this in most of their documentation and marketing but their CTO's blog[1] links to a paper that mentions "obtaining significant throughput improvements over the base MySQL code base from which we started," and given how tightly they mirror MySQL with things like version numbers and goofy configuration flags that only exist for backwards-compatibility reasons, it would be hard to believe they built it from scratch.
GPLv2 and v3 both allow this because they only require source modifications to be made available when the resulting program is distributed outside one's organization. Since the public only ever talks to an interface and never obtains the binary, Amazon doesn't have to redistribute. This is not true of the AGPL, which has additional redistribution requirements meant to prevent (what copyleft activists perceive as) this kind of abuse.
There's an argument that since Amazon's changes are focused around integrating the storage layer with their particular infrastructure, the general public would find their changes useless even if they were to be distributed. Personally don't think this is terribly relevant to the larger discussion around licensing, even if it's true.
[1] https://www.allthingsdistributed.com/2017/05/amazon-aurora-d...