I always had the impression that the benefits only applied if your boarding pass had a QF flight number. I have always booked my KLM flights through the Qantas call centre (classic rewards), so did have a QF flight number. As I said, it has always been my impression. Whether I read it somewhere near the time of launching or whether I just assumed, but I have always just walked up to check in and the staff have taken the extra bag. "Priority" was actually printed on the boarding pass.
However, back then I thought the rules were quite explicit that entry to KLM lounges was not an included benefit, but I note in the 2020 AFF article that I just re-read, that it actually is! I am flying AMS-HAM and return in June on QF flight numbers. One flight departs at 6:30am, so at least I can eat a bit of breakfast in the lounge. My major interest is the extra bag, though. The Fiji call centre didn't ticket one of my J classic reward seats and only Y was available by the time I returned to Australia and realised.