A typical use-case for the AI Chat sidebar, at least for me, is to open it, chat, close it, browse a bit more, go back to the sidebar, chat some more.
However, as soon the sidebar is minimized the web page is closed and your chat history is lost.
On a small (13") screen, the side panel takes up a considerable amount of horizontal space so it is not convenient to keep it open.
But more importantly, the current behaviour is not compatible with how all these AI Chat providers work now - y...