Glad we've narrowed down the abilities to a short list. I'll give my thoughts on each one.
Magic Guard: My personal top choice. It nullifies the two biggest weaknesses to CAP 32. (hazard weakness and mediocre stats) There are three potential issues I see with Magic Guard, though. For one, it may end up being too strong. This can be easily kept in check, however, by its lower stats. Because of these low offensive stats, it is then essentially forced to run Life Orb to have any sort of offensive pressure whatsoever, which might be a bit centralizing. But even if it didn't have Magic Guard, CAP 32 would nearly always run Boots anyway to attain just one of its advantages. Regardless, CAP 32 is going to run either Life Orb or Boots every time depending on which ability we choose. There's a reason the only way a Stealth Rock-weak Pokemon can usually flourish without Boots is if it has insane power like Volcarona/Blacephalon, which won't really apply here. A third potential issue with CAP 32 is that it might be a bit boring. Magic Guard might admittedly a bit of a vanilla pick, and there have already been two CAP Pokemon with that ability. However, I think it could definitely set itself apart from the crowd, especially if it gets access to Flare Blitz.
Adaptability: As I've mentioned before, Adaptability gives basically the same boost as MGLO. While Adaptability is ever so slightly stronger, I'm not sure the difference is enough to justify it over MGLO. Additionally, MGLO provides boosts on all moves, not just STAB. While there are arguments against Magic Guard for it either being too strong, too centralizing, or too boring, in a pure vacuum this ability is simply suboptimal to Magic Guard in my opinion. One possible argument I could see is that MGLO is weaker to Knock Off than Boots+Adaptability, as once it loses its item it loses most of its offensive pressure. I think this is true to an extent, but the fact that CAP 32 is weak to rocks does admittedly severely diminish its potential as a pivot anyway. As long as rocks are kept on the field, it is essentially as useless as MGLO w/o Life Orb.
Pixilate: I really do like this ability, especially since we don't have any boosting moves on CAP 32. To be completely honest, I don't see why we can't just end up with both MG+Pixilate. While Magic Guard might be much stronger than Pixilate and therefore used much more, I feel like the option itself helps it to function better as a pivot as it could bluff Pixilate E-Speed to force out Pokemon such as Dragapult or Roaring Moon. And even though Magic Guard might be stronger overall, the fact that several common fast threats are weak to Fairy does give Pixilate a niche.
Levitate/Earth Eater: Between the two, I personally prefer Levitate over Earth Eater, simply because Levitate is immune to all hazards barring rocks if Boots are knocked off, allowing it to function slightly better as a pivot. Most teams will likely be wary about clicking ground moves against a team with Earth Eater anyway, so the recovery aspect isn't really useful. In the end I'm just not sure that teams that want a ground immunity will run CAP 32 over Pokemon such as Venomicon or Equilibra. It's definitely nice for have a pivot to have an immunity, but I personally don't think that removing one weakness is enough to benefit a Pokemon with mediocre stats.
Prankster: I think I like the idea of Prankster more so than the ability itself. Prankster Parting Shot on a Pokemon advantageous against Gholdengo definitNoely seems fun. However, in the absence of boosting moves, I don't see this ability giving it any offensive pressure whatsoever. Additionally, while Prankster Wisp/Sap/Recovery is nice, I feel like this Pokemon with Prankster might be a free switch-in for special attackers, especially with its low offensive pressure. One way to circumvent this would be screens or moves such as Thunder Wave, but I feel like at that point the only reason to run CAP 32 over Grimm is beating Gholdengo, which I don't think justifies its use enough.
Electric Surge: While fundamentally this ability is useful in a Tapu-free metagame, especially one with Quark Drive, I feel like we should slot terrain abilities for a Pokemon that is physically designed to set terrain. This ability admittedly feels like more of an afterthought, and probably wouldn't even be up for discussion in a metagame with Tapu Koko. Additionally, I just don't think CAP 32 will be able to take advantage of its own terrain enough to warrant its inclusion here. Again, I think if we want to go the terrain route, that should be the fundamental concept behind the Pokemon's competitive design and not something we splash on in the middle of the process.
Sharpness: I think I would be more on board with this if Fairy has a move boosted by Sharpness, but I think the ability is just too one-note for this Pokemon.
Poison Touch: Personally not a fan. I don't see this being really that useful in the long run, especially since it has mediocre stats to begin with. Most Pokemon that get the ability don't even run it anyway.
Regenerator: Honestly, I don't think Fairy over Dragon is enough justification to use CAP 32 over Astrolotl, unless we design it to be functionally the same, which seems a bit boring.
Snow Warning: I have pretty much the same views on this as Electric Surge. Snow Warning could absolutely be useful in this metagame, but I feel like this concept should have come first rather than as an afterthought.
Edit: Noticed a lot of people have vouched for Parental Bond. I like the concept, just not sure how useful it would be in a metagame dominated by Venomicon-P.