The ticketed baggage allowance will indeed cross over to all carriers in the itinerary. The OP is entitled to 2 Pieces max 32Kg for the entire journey which is the business baggage allowance
That Qantas will allow extra luggage beyond the ticketed allowance, does not apply onwards. The Sapphire baggage benefit is for 2 pieces, not 3
As it states on the QF baggage allowance page at
https://www.qantas.com/au/en/travel-...requent-flyers
Originally Posted by Qantas
Some Qantas Frequent Flyer and Qantas Club members are entitled to an additional non ticketed checked baggage allowance. This allowance applies to travel on:
Qantas and QantasLink operated flights with a QF flight number (excluding services to and from Lord Howe Island and QF codeshare services).
Emirates operated flights between and within Europe, The Middle East, North Africa, Asia, New Zealand and Australia when booked with either a QF or EK flight number on your ticket.