My take on this is below ;
View attachment 438494
The above screenshot from QF website says that "if your
final ticketed
origin/destination is within the
USA/Canada, the airline whose flight number appears for the
first flight on your ticket will determine whether it's baggage rules or another airline's baggage rules will apply to all flights in your itinerary" - My understanding so far is that the OPs final origin is in the USA (LAX) and the first flight in the whole itinerary is a QF number (codeshare EK). So QF's baggage allowance should apply for the whole itinerary. Additionally, given that the final origin is LAX (which is in the USA), baggage allowance is calculated as piece based rather than weight based.
Now, take the above information and look at the table below - OP is QFF-SG, flying Y (I assume), gets 3 bags with 32kg max per bag.
View attachment 438495
Happy to be corrected.