Is 2 hours 40 minutes enough for separate international tickets at Sydney Airport?

If a missed onward flight would be expensive, allow a longer connection or an overnight stop. Separate tickets may not include protection when the first flight is delayed.

Ask the airlines whether they can through-check the bag on your actual booking, and confirm the second carrier's latest acceptance time. Plan assuming they cannot.

This is a high-risk connection because you must enter Australia, collect the bag and meet the next airline's check-in deadline. A frequent-flyer status does not remove those steps.