No, it's not grammatically correct, it's just cutesy online cat speak.

Folks also like to speak in a cutesy but deliberately incorrect way when it comes to cats or dogs.

So yeah, chalk this one up as another 'smol', 'angy' or 'feetsies'

Cats’ language proficiency usually doesn’t develop past the level of a typical human toddler. There are exceptions, like Garfield, but most will mispronounce many words and often use incorrect grammar.

Not formally, no. But people regularly say things like “my friend and I’s…” so the future is uncertain.