Well, it took a while but here's what worked. I had to spend some quality time learning more about JSON nested objects and how to process them. I found this website particularly helpful. The code is:

temp = json.loads(response.message.content)

df = pd.json_normalize(temp['pets'])

Here's the output as a pandas df:

   name animal  age  color  favorite_toy
0  Luna    cat    5   grey          yarn
1  Loki    cat    2  black  tennis balls