I've just got every single snake (excluding store snakes but I know those don't count because I have completed years for other pets where I don't have any store ones), and it's saying I'm missing one from the Internet event. I'm not, and under it it shows I own every pet listed as a snake (Including a Parrot for some reason but I'm assuming that's just cause it's grouped with that section, but I also own the parrot so it shouldn't matter anyways.)
I don't know and I'm very paranoid that somehow the archive is missing a snake but according to the individual checkmarks, I have them all