You won't see a true next-gen game for either of the platforms until mid to end of the new generation cycle. Such examples are God of War, TLOU 2 for PS4 and Sea of Thieves and Gears 5 for Xbox One. In PS5's and XSX case i think it will be at least till 2022+ for real next-gen games to start coming out so we are looking at Awoved, Fable and whatever Sony releases in that same time period. Closest thing we have right now next-gen games is prolly R&C and Horizon Forbidden West, for the XSX it would be Hellblade 2, Fable and Awoved when I can start saying we are officially in next-gen (Personal subjective opinion) , but for now we have to enjoy glorified 3rd party cross-gen releases just look, feel and play better on the newer consoles. I do not even consider Cyberpunk 2077 a next-gen game at this point.
For me, my 1st next-gen game was God of War (even though Bloodborne was my GOTY) followed by Sea of Thieves and TLOU 2 if we are strictly speaking exclusives here. As for 3rd party titles its really hard to say because there are so many good games out there that released in between all the exclusives.