Side chats don't allow multiple modes

I used /btw to create a side chat during plan mode while the plan was pending approval. The new side chat was in plan mode, but it didn't actually do anything. It didn't respond to my prompt, presumably because it was pending plan approval, but that seems orthogonal to the plan. Also, if I change the mode from Plan to Interactive in the side chat, which I want in order to review the plan, it changes the mode of the main chat. So I can have two chats in a session which have different modes.