I selected "chats" from the left panel (codex/snioppets/chats), "+ new thread", and then "select AI" -> "edit prompts". The chat stays open, and the prompt settings open underneath the chat.

In other places, "edit prompts" navigates you out of where you are and to the prompt editor, so dismissing the chat would make sense. I could also see pinning the chat, to force the two panels not to overlap. But I do see that pinning is forbidden for empty (?) chats.