Tie break timer and main block timer together

- Starting break now pauses the main block timer (frontend optimistic +
  backend implicit pause event recorded before break_start)
- Resuming/starting the main block while break is active pauses the
  break timer and exits break mode on all clients including TV
- Timer display counts negative past zero so overtime is visible while
  label stays "Done!"
- Fixed WS start handler incorrectly skipping break-mode clear when
  restarting the same block; resume handler now also clears break mode

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/routers/sessions.py

@@ -191,18 +191,30 @@ async def timer_action(
     BREAK_EVENTS = {"break_start", "break_pause", "break_resume", "break_reset"}
     if body.event_type in BREAK_EVENTS:
         block_id = body.block_id or session.current_block_id
-        event = TimerEvent(
+
+        # When break starts, implicitly pause the main block timer so elapsed
+        # time is captured accurately in the activity log and on page reload.
+        if body.event_type == "break_start" and block_id:
+            db.add(TimerEvent(
+                session_id=session.id,
+                block_id=block_id,
+                event_type="pause",
+            ))
+
+        db.add(TimerEvent(
             session_id=session.id,
             block_id=block_id,
             event_type=body.event_type,
-        )
-        db.add(event)
+        ))
         await db.commit()
         await db.refresh(session)
 
         break_elapsed_seconds = 0
+        block_elapsed_seconds = 0
         if body.event_type in ("break_start", "break_reset") and block_id:
             break_elapsed_seconds, _ = await compute_break_elapsed(db, session.id, block_id)
+        if body.event_type == "break_start" and block_id:
+            block_elapsed_seconds, _ = await compute_block_elapsed(db, session.id, block_id)
 
         ws_payload = {
             "event": body.event_type,
@@ -211,6 +223,7 @@ async def timer_action(
             "current_block_id": session.current_block_id,
             "is_active": session.is_active,
             "break_elapsed_seconds": break_elapsed_seconds,
+            "block_elapsed_seconds": block_elapsed_seconds,
         }
         await manager.broadcast(session.child_id, ws_payload)
         return session