The conversation pane had no scroll management at all - it opened at
the top of history, ignored arriving messages, and offered no way back
down other than dragging through long replies.
- Opening a conversation lands on the newest message (the component is
keyed by space, so mount = open)
- A reader at the bottom stays pinned as new messages arrive; a reader
up in history is left undisturbed
- The moment the reader leaves the bottom, a floating "Jump to latest"
pill appears above the composer; clicking it smooth-scrolls back and
the pill hides itself again
- The scroll region is a proper role="log" landmark; e2e seeds a dozen
multi-line messages over real IPC, scrolls to the top, and drives the
pill's appear -> click -> return-to-bottom -> disappear cycle