Pre-pandemic, SYD used to have an Express Path lane and paper express path slips were handed to first & business class passengers plus top-tier frequent flyers – but that's since been replaced by a Priority Lane which is primarily intended for first & business class, and when flying in those classes your boarding pass – either paper or digital – is endorsed with 'Express Path'. SYD says it's considering opening up the Priority Lane to frequent flyers based on a per-airline arrangement if airlines pay for it (eg % of the staffing costs would be a baseline)

Note that all airlines say they are not offering Priority Lane access to frequent flyers based on status alone (eg in premium economy or economy), although I know quite a few top-tier frequent flyers who have upon checkin at the airport had their boarding pass endorsed for the priory lane.