Thanks for posting @oliver.espeter and welcome to Kong Nation!
You’ve pointed out a great thing for us to look at how we can update. In short, Postgres has been “very good” about not introducing breaking changes for a very long time as far as Kong’s code is concerned, so in some ways, an update hasn’t been super-critical. However, I agree using old versions in docs, etc, isn’t a good user experience either, so we’re going to look at updating those.
We see users running successfully with 13.1, so I suspect you’ll be fine, but this is an area of testing we need to expand to better validate for users like you. Regarding RDS, we do not currently test against Amazon RDS though, so that may continue to be a “TBD” even after we start varying our test infrastructure.