Stop and start a session's process from the composer

The composer's second button now says what pressing it would do to the
process behind the session, in one place that is always there: an orange
pause while a turn is running (interrupt, the process stays), a red stop
when it is not (end the process), a green play when it has exited (start it
again on the same conversation). Send is disabled while there is nothing to
send, rather than pressable and silent.

Behind it, two routes. `stop` signals the recorded process and says nothing
else -- the driver's own reader already reports a death correctly, and
announcing it here would be a guess ahead of the measurement. `start`
replaces the driver and nothing else, so the transcript, the pump and every
open phone's stream stay where they were and there is still one writer of
the transcript; it is refused unless the session is known to have exited,
since starting on `Unknown` is the two-CLIs-on-one-conversation fault.

That last rule found a bug in the launch path: a relaunched session took its
status from the transcript, so one whose process had died before a backend
restart reported `exited` while the launch had just started a new process --
which refuses every command and offers a phone the chance to start a second
CLI on a live conversation. A launch that leaves a process running now says
idle.

The icon font moves to the Mono face, where every glyph is one em square, so
two icon buttons are the same width without either being told one; the
proportional advances ran 0.46 to 0.92 em and Send came out visibly wider
than Stop. GLYPH_SIZE comes down to match, since a glyph that fills its em
draws bigger at the same point size.

Verified against a stand-in CLI on the emulator: idle -> stop -> exited ->
start -> idle, a turn interrupted from the pause button, and both buttons
measured at 171x105 device pixels.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

server/src/routes.rs

@@ -17,7 +17,9 @@
 //!                                      `reset` frame plus the newest window)
 //! POST   /sessions/{id}/message        {text, attachmentIds?}
 //! POST   /sessions/{id}/answer         {questionId, answers}  (questions and permissions)
-//! POST   /sessions/{id}/interrupt
+//! POST   /sessions/{id}/interrupt      stop the running turn; the process stays
+//! POST   /sessions/{id}/stop           end the process; the session and transcript stay
+//! POST   /sessions/{id}/start          run the process again, continuing the conversation
 //! POST   /sessions/{id}/title          {title}
 //! POST   /sessions/{id}/model          {model}
 //! POST   /sessions/{id}/command        {text}  -- /compact, /clear, /rename x, or the dialect's own
@@ -87,6 +89,8 @@ pub fn router(manager: Arc<SessionManager>) -> Router {
         .route("/sessions/{id}/message", post(message))
         .route("/sessions/{id}/answer", post(answer))
         .route("/sessions/{id}/interrupt", post(interrupt))
+        .route("/sessions/{id}/stop", post(stop))
+        .route("/sessions/{id}/start", post(start))
         .route("/sessions/{id}/title", post(rename))
         .route("/sessions/{id}/model", post(set_model))
         .route("/sessions/{id}/permission-mode", post(set_permission_mode))
@@ -678,6 +682,31 @@ async fn interrupt(
     Ok(StatusCode::NO_CONTENT)
 }
 
+/// Ends the session's process. The session stays, and `start` brings it
+/// back -- see [`SessionManager::stop_session`].
+///
+/// Not `lookup`ed: a session that failed to relaunch has no live entry and
+/// may still have a process running, which is exactly one worth being able
+/// to stop.
+async fn stop(
+    State(manager): State<Arc<SessionManager>>,
+    UrlPath(id): UrlPath<String>,
+) -> Result<StatusCode, ApiError> {
+    manager.stop_session(&id).map_err(bad_request)?;
+    Ok(StatusCode::NO_CONTENT)
+}
+
+/// Starts a process for a session that has none, continuing the same
+/// conversation -- see [`SessionManager::start_session`], which refuses
+/// unless the session is known to have exited.
+async fn start(
+    State(manager): State<Arc<SessionManager>>,
+    UrlPath(id): UrlPath<String>,
+) -> Result<StatusCode, ApiError> {
+    manager.start_session(&id).map_err(bad_request)?;
+    Ok(StatusCode::NO_CONTENT)
+}
+
 /// The usage screen needs two things that live in different places: the
 /// cache, and the current list of machines to ask. Carried together rather
 /// than the monitor holding the manager, which would point the dependency