Does AWS Aurora actually use postgres or is it simply a postgres compatible API on top of their own technology?

As with RDS Postgres, it's Amazon's fork of Postgres.

With Aurora, the storage layer is swapped out entirely for a distributed storage engine, that I believe is based upon DynamoDB.

The wire protocol and server interface are much the same as regular Postgres, though there are some additional benefits as well as caveats as you might expect

I'm pretty sure it's a fork of PG based on my experience.

this is a huge issue for us and I'm extremely unhappy this was not clear in the docs

What's worse is the documentation straight up lies. It states you can perform a major version upgrade by resorting a snapshot and selecting a higher version. I mean it's still not ideal except if you do try this you'll find the option doesn't actually exist - either via the console or API/CLI!

https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide...

This has really put us off using other AWS managed products and was a major factor in us deciding against using Amazon Elasticsearch Service.