I've seen the hidden combat log on the right side of the screen, but I only see rolls being logged there. Is there a similar log for chat, or an option to turn it on that I missed?

Several times I've been moving my map around while my characters were walking in the crypt and they came across something that rolled a perception check and I missed what they said about it because my map wasn't focused on them. I've reloaded multiple times just to be able to see what the perception check was. Even with them saying it out loud, it doesn't always register with me what they said if I'm studying the map and not expecting them to start talking. It would also be nice to be able to scroll back through the history of the zoomed in "cinematic" dialog parts to be able to review what I chose and the consequences.

Yes, had the same issue, didnt catch what they said so had no idea what to look for. Chat window would be a very good addtion

There’s a chat history button in the right when you’re in convos, but it only has it for that specific convo.
Otherwise you can check your journal.