How can we publish Aurora (Postgres compatible) logs to Cloudwatch?
Full Disclosure: I am the product manager for Aurora PostgreSQL.

We are working to add support for the feature you noticed that is already available for RDS for PostgreSQL and for Aurora MySQL, to automatically copy database logs to Cloudwatch. While I don’t have a date to communicate, we plan to launch this feature soon - stay tuned!

Kevin Jernigan
Principal Product Manager, Amazon Aurora with PostgreSQL Compatibility