Everything can be incorporated into your character's RP - pets, artifacts, clothing, curios, skills. They're all available as hooks or platforms to develop your narrative. I love interacting with people's pets, personally, and by default I consider them separate entities from their owners with their own personalities and histories. Even pets that are played as extensions of their owners' psyches, like Luce's Kaiyo and Tikki's Kosuke, can have distinct voices, and it's a lot of fun to see how they differ from their owners.
My custom beasts have always had sentience, but I've never had them speak. I've enjoyed the challenge of conveying their personalities through emotes alone, and it also saves me the trouble of having to verbally articulate their world views.