Agents: cannot close the session's main chat tab

In the Agents window every chat tab can be closed except the session's main chat — it renders no close button.

https://github.com/user-attachments/assets/58e8de18-fee2-4c14-8c92-d05a087a0079

I know this is actually the current decision — the main chat is treated as the session itself and closing it is deliberately blocked — but I think it's better the other way round. Closing should just hide the tab like any other chat, as long as the session keeps at least one visible tab. Nothing is lost: the chat stays reopenable from the Chats picker.

Start by reproducing the Agents window behavior and tracing how chat tabs decide whether to render a close button. Compare the session's main chat with other tabs and the Chats picker; done means the main chat can be hidden while at least one visible tab remains and can still be reopened.

Written by the indexing model from the issue text.