As others have mentioned, the one area your new camera wins over a phone is with its optical zoom. Think about composition. You should be able to come back with portraits - closeups - of animals but also context or environmental shots where you can show the animals in a particular habitat. All animals have personalities so pay attention to when they're exhibiting interesting behavior and try and capture that, if possible. Pay attention to how the light is falling on the scene and adjust your position to capture the best angle, if possible. Light and shadow always makes images interesting.
It's a fact that P&S sales have decreased dramatically as have the sales of all dedicated cameras. There's no "prove it" discussion needed, as there are endless articles for you to review and industry numbers to back them up. Many of those articles will attribute that decline - rightly so - to the advance in phone capabilities. And phones take stunning images, shoot raw, shoot amazing video and provide a lot of control over the final output in the right hands. That includes control over the light as you can even control certain flash units with phones. So the kinds of P&S that do sell well given the volume will be ones that have a clear advantage over the phone. In general, for the types of subject I shoot, there's one advantage: Optical zoom. That's about it (again, for me).
Note that "dramatic decrease" does not mean, nor does it imply, "zero". P&S cameras are still selling. Just not nearly in the same numbers. Again, you can look that up. Likewise, Best Buy still makes some money selling P&S cameras. Just not nearly what they did a decade ago. In my local one, the camera section is a shadow of what it was in 2011. If you went and rephrased your question to your sales friends to something like: "What do you sell more of, P&S cameras or phones?", the answer would be more telling.
At the end of the day, literally none of this matters. What matters is that you have a camera you like and you're going to shoot images of animals at the zoo! Sounds like a lot of fun to me, especially with that optical zoom. Come on back when you're finished and start sharing some of those photographs.