When busy_input_mode is 'steer' and the steer is accepted by the server,
show a transient indicator in the chat area (not in S.messages).
This mirrors the CLI/Gateway approach: steer text is never stored in the
message array. The done event's S.messages=d.session.messages replacement
therefore doesn't cause a flash where all SSE content vanishes and re-appears.
The indicator is an independent DOM element (.steer-indicator) appended to
msgInner. It naturally disappears when renderMessages rebuilds msgInner on
turn completion (done/cancel/error).