They’re like birds, right? Don’t they have a cloaca instead?

searches

Apparently yes, though this author couldn’t resist “butthole”…

https://www.livescience.com/first-dinosaur-butthole-found.html

1st preserved dinosaur butthole is ‘perfect’ and ‘unique,’ paleontologist says

This was a multipurpose hole.

The first dinosaur butthole ever discovered is shedding light where the sun don’t shine. The discovery reveals how dinosaurs used this multipurpose opening — scientifically known as a cloacal vent — for pooping, peeing, breeding and egg laying.