I wonder if the cat is indeed Leticia.
To be fair, we don't have much of an explanation on what beastkin are nor why Glenreed, who doesn't have any external traits indicating that he is a beastkin, can transform into a wolf so perhaps this cat is indeed Leticia. We do know that Glenreed had a strong sense of smell even as a human. In fact, in a country where royalty chooses beastkin and human princesses, there's no doubt the royal family had human and beastkin blood.
Perhaps many of the humans in this country are actually capable of transforming into an animal form but also into a full human form while beastkins are just stuck in between, perhaps beastkins can also transform fully into an animal but not a human.
But it would be weird for Leticia's entourage to be unaware that she can transform. If it is the case that Leticia is the cat, I'm guessing that they are keeping it a secret and keeping her food traditionally western and heavily spicy to ensure no one doubts that she is fully human. Well, the four families definitely have some ancestors from the central royalty, which means that the human families have some beastkin blood and the beastkin have some human blood. I guess it makes sense that some members of the human families end up having some beastkin abilities.