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For those who care, a visual list of all the Gen I-IV mons who can now be in the Apricorn Balls. Notably, only Drifloon and Drifblim were completely unavailable in HGSS and available in SM. Every other single Pokemon on this list were in HGSS, just not in Apricorn Balls. Aside from the Johto Starters and the gifts, nearly all of the Gen III and IV ones are due to only being available in places where you couldn't use the Apricorn Balls, despite being catchable in HGSS. Places like the Safari Zone (Safari Balls only) or the Poke Walker Courses (Normal Poke Ball only). A few were only available in the Bug Catching contest, meaning they could only be in Sport Balls.
Shellos and Gastrodon are weird, because only Eastern Sea were in HGSS, but only in the Poke Walker so they couldn't be in Apricorn Balls. Only Western Sea are natively in SM, but I don't know if you can pass down Apricorn Balls if you breed a Male Western and Female Eastern pair of Shellos or Gastrodon.
Also, though I didn't add them, Bonsly and Sudowoodo are available in SM to be caught in Apricorn Balls. They technically were in HGSS, but there's exactly one catchable Sudowoodo, and Bonsly only from the Walker, and it's both fairly early on and something you need to get out of your way to continue on. So you're unlikely to have Apricorn Balls then. I can't find a lot good info on it, but apparently it can respawn post-Elite Four, but only if you didn't catch it when you first fought it.
Obviously, the Gen V and VI Pokemon available in SM are also now legal in Apricorn Balls, but there's no reason to list them as there were never any games before this one that had Apricorns and they existed in. The only one that you can't put in an Apricorn Ball is Zygarde, as it's sort of a gift mon due to how you get it. All Gen VII Pokemon aside from the Starters, Silvally, and the events are also legal in Apricorn Balls.
Now if only you didn't get exactly one chance per game.