I think one problem with the idea of learning the language of captive animals is that it runs on the assumption that animals have an inherent language. There was some research centuries ago that involved raising kids without exposure to the outside world of languages in hopes of learning what our "natural" language was. Turns out there isn't one.

And I think the same applies to animals. Bird songs have already been noted to have accents by region. We'll probably end up finding out that if animals do have complex language, it's something they develop through community exposure just like humans do, and it'll vary by area. Crows in Texas will talk very different from crows in England, I'm sure.

With pets, most of them are kept isolated from the world at large. It wouldn't surprise me if dogs raised by people have very stilted or nonexistent language compared to feral dogs. Maybe 200 years from now, we'll see the modern concept of raising dogs completely alone as inhumane and sending them off to doggy daycare a couple times a week to learn the local dog language and "culture" will be normalized.