I have arrived internationally at SYD a few times this year, latest on Monday just after the pre-departure test requirement removed. As of last weekend, the online DPD form hadn't been updated to remove the pre-departure test requirement, so I just ticked "exempt" as I was arriving just after the 18Apr/00.01 rule change and form was approved. Hopefully updated now.
Downloads confirming completed DPD and Vaccination Certs were verified at overseas check-in and that was it - no health docs requested on arrival in SYD other than the standard orange customs & health form distributed on-board before landing.
As above, states may have their own entry requirements - for NSW it was to do a self-admin RAT test within 24 hrs and to keep away from certain high-risk environments, but assuming arrival into SYD you can find details online as below or you'll get usually get an announcement re the latest from cabin crew or a local health official just before you disembark.
Usual advice to carry hard copy prints of your documents rather than just electronic.

https://www.health.nsw.gov.au/Infectious/factsheets/Pages/arrivals-guidelines.aspx