Interesting observation about your dogs - never had any or cats. I suspect in the early stages of any learning that AI might do, such will be more about intent, and as to this often being obvious in many species. As you mention, dogs seem to be able to read our intent through perceived emotion and such often being recognised by our tone of voice. Even if we discover that many species have hardly much worthwhile in their communications, this should be better than what we currently have - often just ignoring it. I'm sure much will be rather mundane though - as per much of human communications.In my experience with dogs, one can communicate with them, but via a type of blue tooth connection, associated with feelings. Humans mostly use word commands to create parallel emotions to the words. The animal senses the feeling, and this helps attach the word.
The human brain, when it writes to memory adds emotional tags to sensory content. With animals we induce the feeling first, and the word, by being a type of audio content, gets tagged for memory storage. Words can convey emotions; sit (stern warning) and point (visual cue) adds to the writing process.
With my Belgian Malinois, I invented a command I called "all done". This nebulous command meant that whatever we/he was doing, "all done", meant it was time to change what he are doing, no matter the circumstances, and do something new. He learned this open command and could be redirected from any behavior or fixation on any occasion. It worked because I originally associated all done and change to something new and fun. He associated it with happy to learn. This breed has very high adaptive intelligence. They can learn highly adaptive commands.
In a few experiments with my dog, I would use the learned command words but alter the emotion behinds the word to se if he reacted to the word or the new emotion. Bad dog with a playful smile and good dog with an angry voice, would reverse the meanings on command.
Sometimes, even today, if I am thinking and come to an exciting realization in my thinking, that causes a stronger inner feeling, my two smaller dogs will bark and start to act like an intruder is nearby, even from the other room. This may be connected to many years of censorship to new ideas. They feel a ping, and try to warn me of danger. I may tone down.
Language is newer than the domestication of dogs, so how did humans and dogs communicate before spoken language? The dog would associate visual cues based on human emotions. This is where AI has no clue, since machines lack feelings, Feeling are critical to writing to memory within animals. The AI will need a human to generate the feelings as an intermediary to words.
I'm sure dolphin communication should be interesting to unravel though - and perhaps most of the more social species - but I doubt anyone is expecting to have much in the way of intellectual discussion with any.