I dont know this for a fact, but I suspect it has to do with the fact your 2021 Model Y likely has "from the factory" DATA usb ports in the console, while the 2023 Model 3 does not have data in the console from the factory.
By "console" I mean the console in between the driver and passenger seat (just for clarity, you likely knew this).
For the cars that did not have USB data in the console, the only USB port with data was in glove compartment, and that one, from the factory, has the Sentry mode flash drive (provided by Tesla) in it. Tesla does not officially support any USB docks at all, so in effect, there is no port to plug in a controller in cars that do not have USB data from the factory.
Thus, tesla flags these cars and does not make any games available that need a controller to play. There are a few different threads here that the above is true (games missing for vehicles that didnt have USB data from the factory), so I feel fairly comfortable connecting those dots.
Tesla was supposedly working on making bluetooth controllers work in these cars, and I think they have done so, but I am not following that discussion because I dont care about the games pre loaded in the car. I dont spend any time at superchargers, and have my smartphone, or a nintendo switch, should I really want to game on the road.
Its likely that these cars (without data in the console from the factory) are flagged as such in Teslas system, so some games are automatically not available (Tesla likes automation wherever possible so would automate this).
Anyway, the TL ; DR is most likely "your 2023 did not come with data ports in the console from the factory, and is likely flagged as such.
My 2021 does have data USB, but the 2023 also has games that require controllers (prior to this update). I was just wondering if it was a licensing issue.
For instance, the 2021 (SW 2023.20.9) has:
Polytopia, Mahjong, Sudoku, Sky Force, Solitaire, CatQuest, Fallout Shelter, Stardew Valley, Backgammon, Cuphead, Beach Buggy Racing, Chess, 2048, Asteroids, Centipede, Superbreakout, Lunar Lander, Missile Command, Millipede, Tempest, and Gravitar
The 2023 (SW 2023.26.7) has:
Vampire Survivors, Polytopia, Mahjohng, Sudoku, Sky Force, Solitaire, CatQuest, Fallout Shelter, Stardew Valley, Backgammon, Cuphead, Beach Buggy Racing, Chess, and 2048
Now that I've listed them all out, I think its all of the Atari games that are missing.... (Asteroids, Centipede, Superbreakout, Lunar Lander, Missile Command, Millipede, Tempest, and Gravitar).
NOTE: Vampire Survivors isnt on the 2021 because I havent gotten 2023.26 on that yet. I wonder if 2023.26 gets rid of those or if they just never get installled on the 2023.