But classic reward seats are marketed by the operating airline.
Correct, if a Qantas Club member traveling in Economy was travelling from Brisbane to Nadi and redeemed points for FJ920 they would not get lounge access however if they booked a cash fare via the Qantas website on QF3873 they would.
Some partner awards like Air Calin and Air Tahiti Nui book on to the QF flight number which can be a benefit for Qantas club members.
The one exception which seems to be a recent change is that Emirates flights (EK flight number) departing from Australia only, QF Club members get access to the Qantas lounge (but not the Emirates lounge) where applicable (ADL, BNE, SYD, MEL) - not Perth due to different terminal.
Also for revenue seats, where they are available, booking with the QF flight number may cost more than booking directly with the operating airline.
Correct however that is the benefit one gets for booking on the QF flight number. For the record that doesn't just apply to Qantas Club members but also those with Gold/Platinum status (when travelling on Qantas partners who aren't apart of the oneworld).
There are quite a few of these that exist:
Air France - QF Club/Gold/Plat get access to the SIN or HKG Qantas lounges prior to QF codeshare flights to Paris. Gold/Plat also get access to AF lounge departing from Paris (but not for QF Club).
Air New Zealand - QF Gold/Plat get access to Air NZ domestic lounge when booked on a QF flight number NZ operated flight (not for QF Club).
Air Tahiti Nui - QF Club/Gold/Plat get access to the AKL and LAX lounge prior to QF codeshare flights to Papeete.
Air Vanuatu - QF Club/Gold/Plat get access to the BNE/SYD/MEL lounge prior to QF codeshare flights to Vanuatu.
Air Calin - QF Club/Gold/Plat get access to the BNE/SYD/MEL and the Air Calin Noumea lounge prior to QF codeshare flights operated by SB.
Air North - QF Club/Gold/Plat get access to QF domestic lounges prior to Air North operated QF marketed flights.
Bangkok Airways - QF Club/Gold/Plat get access to the SIN QF lounges on QF codeshare flights to Koh Samui.
China Airlines - QF Club/Gold/Plat get access to the BNE/SYD/MEL lounge prior to QF codeshare flights to Taiwan.
China Eastern - QF Club/Gold/Plat get access to the BNE/SYD/MEL lounge prior to QF codeshare flights to China. Gold/Plat also get some other lounges/perks.
China Soutern - QF Club/Gold/Plat get access to the BNE/SYD/MEL lounge prior to QF codeshare flights to China.
Emirates - Emirates as mentioned above is an odd one out, QF Club gets access to AU Qantas lounge regardless of QF or EK flight number and in Dubai the Emirates Business lounge but only on a QF flight number. Gold/Plat get access everywhere.
Fiji Airways - QF Club/Gold/Plat get access to the QF lounges in BNE/SYD/MEL/ADL/LAX/CBR/AKL/CHC/HKG/HNL/SIN/WLG and the Nadi lounge prior to QF codeshare flights operated by FJ.
KLM - QF Club/Gold/Plat get access to the SIN or HKG Qantas lounges prior to QF codeshare flights to Amsterdam. Gold/Plat also get access to KL lounge departing from Amsterdam (but not for QF Club).
LATAM - QF Club/Gold/Plat get access to the AKL/SYD/MEL lounge prior to QF codeshare flights. Gold/Plat also get some other lounges/perks.
Solomon Airlines - QF Club/Gold/Plat get access to the BNE/SYD lounge prior to QF codeshare flights.