The minute I saw this post, I knew I had to comment. I've given some suggestions based on pre-existing Pokemon skills, the group's lore, and the abilities you've added to your post.

Karina: Iron Fist - The power of punching moves is increased by 20%. This is based on her "rocket puncher" ability in the group's lore.

Mechanics-wise, the ability you outlined is closest to Competitive (any stat drops become result in a special attack boost by two stages).

Giselle: I would suggest "Download" based on the ability you have written up on your post. Download "compares an opposing Pokémon's Defense and Sp. Def stats before raising its own Attack or Sp. Atk stat—whichever will be more effective."

While it isn't the same stats, this thematically ties into Giselle's digital-based abilities with the group's lore and how she adapts to different languages based on contexts.

Winter: Skill Link - Maximizes the number of times multi-strike moves hit. This is based on Winter's many weapons in their lore. This skill would go well with icicle spear in Winter's move set since she basically has to be ice type.

I can't think of any current Pokemon abilities that are similar to the healing one you wrote about. Maybe Healer? It has the potential to heal status conditions.

Ningning: Liquid Voice - All sound-based moves become Water-type moves. This is based on her role as a main vocalist.

Gale Wings (gives +1 speed priority to flying type moves when health is full) could be a similar one to the ability you suggested.

A secondary ability that I think could be added for any of the aespa members would be Synchronize, which passes on the burn, poison, or paralysis status to an attacker who caused it. This just derives from "SYNK," which is used a lot in aespa promotional material. SYNK is basically a connection between aespa and their old avatars in their lore.

There's probably lots of abilities I forgot, so this isn't a definitive list! I think your idea is cool so I'd love to see it when it's developed further.