Show timer remaining per block and fix single-click block switching

- Block list on both dashboards now shows time remaining on each block's
  timer (allocated duration minus elapsed) instead of total duration;
  the active block counts down live every second
- Fix block switching requiring 2 clicks: replace separate pause+start
  requests with a single start request; backend implicitly records a
  pause event for the previous block atomically
- Export blockElapsedCache from store so views can compute per-block
  elapsed for both running and paused blocks

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

backend/app/routers/sessions.py

@@ -170,6 +170,17 @@ async def timer_action(
     if not session:
         raise HTTPException(status_code=404, detail="Session not found")
 
+    # When starting a different block, implicitly pause the previous one so
+    # the activity log stays accurate and elapsed time is preserved correctly.
+    if body.event_type == "start" and body.block_id is not None:
+        prev_block_id = session.current_block_id
+        if prev_block_id and prev_block_id != body.block_id:
+            db.add(TimerEvent(
+                session_id=session.id,
+                block_id=prev_block_id,
+                event_type="pause",
+            ))
+
     # Update current block if provided
     if body.block_id is not None:
         session.current_block_id = body.block_id