Yes. I know. That's what my comment said.

I should add that mammals are the outlier here, having subdivided these tasks into separate orifices. Most vertebrates have a single opening, derived from embryological anal opening, which does it all.

https://www.nature.com/articles/s41598-017-09359-y

Yes. And a cloaca is an anus that has taken on additional functionality in some groups. In fact, in mammals the original mammalian ancestor likely had a cloaca, which split into separate openings (in some derived groups). But embryologically it all starts with the anus.

There's a distinct term for it because it serves more than one function. But it developmentally starts as the anal opening, and continues to serve as the anus in an adult. This is really all semantics, but from a developmental biology standpoint it is an anus that has acquired other functionality.

Edit to add, from the Wiki link: "In deuterostomes, the original dent becomes the anus, while the gut eventually tunnels through the embryo until it reaches the other side, forming an opening that becomes the mouth."

Vertebrates are deuterostomes. In bird development, that original "anus" becomes the cloaca.

They do have cochleas (all mammals do). But birds don't.

This is not true. From their earliest embryological development, animals have mouth and anal openings. It's representative of the tube-like critters from which we first evolved. In some animals other orifices develop, but mouth and anus are generally present unless secondarily lost. The cloaca is an anus with additional functions, which is not uncommon in the animal kingdom.