This seems like a book.

Humans extinct for a billion years, AGI and robots tasked to feed and "take care of the cats".

I imagine entire cities, houses built, all empty save cat and humanform robot.

I would recommend the two episodes "Three Robots" and "Three Robots: Exit Strategies" from the anthology series Love, Death and Robots if you like this kind of humor.

You might like the game Stray. Here's the trailer: https://www.youtube.com/watch?v=kJawWyRUOBM

It's about a cat that lives in a city of robots long after humans are extinct.

In the puzzle game series The Talos Principle, intelligent robots (who were made to outlive humanity after a species-ending global pandemic) seem to have the exact same kind of affinity for caring for cats that humans do. It's actually really sweet and cute.

This was a minor plot point in that one black mirror episode with the robots on a tourism trip to Earth, lol

"There will come soft rains" Ray Bradbury