I read it as them treating the initialism "GPT" as an acronym, resulting in "gibbity". I once a YouTuber refer to ChatGPT as "Mr. jip-uh-tee" and I think this is the same idea. I think your definition of "researching using AI" is right, they're just saying it in a joking way.
asqapro
I read a book a while ago called The Annotated Chronicles that included a "boot scene" and the margins included a note from one of the authors about how Kirk inspired the idea. I hadn't seen Star Trek, nor did I know anything about it, so I didn't get the reference until just now. Your meme just resolved a 15-year gap in knowledge for me.
The source I linked for the top plane is the original photo. There's a lot of copies of the edited version with that pinup added, but I couldn't find a definitive original source for who added it.
Source for the bottom: Chelodoy (NSFW)
Non-twitter link: https://xcancel.com/chelodoyart/status/1350928648526835714
(Thanks to Znuffles_ on Reddit for the artist's name)
Edit: Source for the top plane
I rented a room from my boss in college and he pulled this prank on me. First he hid it in the office and convinced all my coworkers to pretend not to hear it. It would switch between a creepy child's laugh to a man groaning to other random noises. I was pretty sure it was a noisemaker, but I couldn't get anyone else to admit that they could hear it so I couldn't confirm.
Then he moved it into the air vents of his house that I was renting a room in. I started to think I was developing schizophrenia since my mom suffered from it and after I confided as much in my roommate / coworker, he finally came clean and showed me where our boss hid it.
All of this to say, it's a very effective prank.
Source: Hitsuji
Non-twitter link: https://xcancel.com/hitsujigoods/status/1567909942639865857
Tap for spoiler
It was for a peanut butter and jelly sandwich
Non-twitter link: https://xcancel.com/hitsujigoods/status/1567925752385122304
Strawbebeh: https://linktr.ee/strawbebeh
And the original post on reddit.