I don't think dogs are a great example of an intelligent species just because we can communicate with them reasonably well. They have evolved to be able to participate in human society. With the exception of some breeds of herding dogs, they're probably stupider than (to pick one example) raccoons. But dogs possess a key trait that raccoons lack: they can understand human emotion reasonably well.

My parent's dog makes them indirectly do what she wants => direct communication is potentially overvalued.

This is almost literally the plot of Arrival :-)

Which is particularly relevant given their similarities to an octopus, albeit a 4th dimensional version of one.

That makes me wonder - do they have what we would consider reasonable conversations with each other?

Chimp communication is complicated enough that it can probably be called conservation, but I think they're one of the only species for which that is true.

I think most animals lack a wide enough range of responses to have a conversation.

In most cases humans have not yet figured out anywhere near the full range of particular animals’ communication, so this is hard to judge.

For example, prarie dogs https://www.nytimes.com/2017/05/12/magazine/can-prairie-dogs...

I’d be happy with dolphins or whales.