> the informal word-button experiments suggest that non-avian animals like cats and dogs
I always wanted to see long form content on this. Like I'm sure the cherrypicked clips make it look more impressive than reality but I've owned enough pets to believe they can understand more than just individual words / tone.
Here is a video that I actually just watched recently on that exact thing.
It's your lucky day
https://www.youtube.com/watch?v=iXJfK1wR_w0
Buddhism, Out-of-Africa, Talking Dogs | Robert Sapolsky Father-Offspring Interviews #96
Research implies that - no, pets don't have complex understanding of word combinations, beyond the usual commands. But, in terms of recognizing words individually - some of the gifted ones show abilities on par with 18-month-old humans.