RightHandCat

The page for Right-Hand Attack Dog makes it seem like Right-Hand Attack Dog is any villainous pet that is an active fighter and Right-Hand Cat is any villainous pet that is passive, but the actual page for Right-Hand Cat makes it seem like the trope is particularly about villains favoring cats, and another animal is not allowed even if it is passive. The note at the end says that an aggressive cat would count as a Right-Hand Attack Dog, not a Right-Hand Cat, but does the opposite apply where a passive dog would count as Right-Hand Cat? Again, the actual page for Right-Hand Cat really makes it seem cat-exclusive. I feel like maybe there should be two separate tropes, one for passive villainous pets and one for villains preferring cats as pets regardless of the cat's role in the story.

Sometimes, the writers may use this trope to parody Ernst Stavro Blofeld, one of the most famous James Bond villains

I agree that "passive pet" and "cat" are separate tropes; the latter perhaps being related to Cats Are Mean.

I mean, unless the "passive pet" stuff is reasonably common, then that's just one trope getting another trope's definition wrong. And if it is reasonably common, yeah, it'd be worth splitting off the misuse.