There's nothing that's all that different between the RX8 and the RX7. Honestly, I'd use 10w-40 dino and I'd also premix the gas with either motor oil or TCW3. The Apex seals need all the help they can get, as those engines are not long lived.
Suzuki had a Wankel rotary engine, but I cannot remember a Honda rotary.
FTR, before I knew better, I ran Castrol Syntec 5W50 in my 12A. I never had any problems which either says a lot about how good the 12A was or how overrated the early Group III Syntec was.
I know better now. Don't use synthetic.
You can use synthetic if you plumb up a separate tank for the oil injection system, and put something like TC-W3 in that tank. That will keep the apex seals happy.
Or just use dino, way less of a PITA. Today's dinos are excellent oils.