Add manual block start and fix timer display labels

Blocks are now selected without auto-starting the timer. Clicking a block
makes it current (highlighted) but leaves it in a ready state. A "Start"
button (indigo) triggers timing for a fresh block; "Resume" appears for
previously-worked blocks; "Pause" remains while running.

Also fixes the sidebar duration label to show "Done!" when elapsed ≥ total
and "< 1 min" for sub-minute remaining time instead of "0 min".

Backend adds a "select" event type that records an implicit pause for the
previous block, updates current_block_id, and broadcasts is_paused=true
with prev_block_elapsed_seconds so the TV sidebar stays accurate.

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

backend/app/routers/sessions.py

@@ -1,4 +1,4 @@
-from datetime import date
+from datetime import date, datetime
 
 from fastapi import APIRouter, Depends, HTTPException, status
 from sqlalchemy.ext.asyncio import AsyncSession
@@ -159,7 +159,7 @@ async def get_session(
         select(DailySession)
         .join(Child)
         .where(DailySession.id == session_id, Child.user_id == current_user.id)
-        .options(selectinload(DailySession.current_block))
+        .options(selectinload(DailySession.current_block).selectinload(ScheduleBlock.subject))
     )
     session = result.scalar_one_or_none()
     if not session:
@@ -178,15 +178,17 @@ async def timer_action(
         select(DailySession)
         .join(Child)
         .where(DailySession.id == session_id, Child.user_id == current_user.id)
-        .options(selectinload(DailySession.current_block))
+        .options(selectinload(DailySession.current_block).selectinload(ScheduleBlock.subject))
     )
     session = result.scalar_one_or_none()
     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:
+    # When starting or selecting a different block, implicitly pause the previous
+    # one so the activity log stays accurate and elapsed time is preserved.
+    prev_block_id = None
+    prev_block_elapsed_seconds = 0
+    if body.event_type in ("start", "select") 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(
@@ -194,6 +196,28 @@ async def timer_action(
                 block_id=prev_block_id,
                 event_type="pause",
             ))
+            # Compute prev block's accumulated elapsed so all clients (especially TV)
+            # can update their local cache without relying on a separate pause broadcast.
+            prev_tick_result = await db.execute(
+                select(TimerEvent)
+                .where(
+                    TimerEvent.session_id == session.id,
+                    TimerEvent.block_id == prev_block_id,
+                    TimerEvent.event_type.in_(["start", "resume", "pause"]),
+                )
+                .order_by(TimerEvent.occurred_at)
+            )
+            prev_tick_events = prev_tick_result.scalars().all()
+            _last_start = None
+            for e in prev_tick_events:
+                if e.event_type in ("start", "resume"):
+                    _last_start = e.occurred_at
+                elif e.event_type == "pause" and _last_start:
+                    prev_block_elapsed_seconds += int((e.occurred_at - _last_start).total_seconds())
+                    _last_start = None
+            # Add the current open interval (up to the implicit pause just recorded)
+            if _last_start:
+                prev_block_elapsed_seconds += int((datetime.utcnow() - _last_start).total_seconds())
 
     # Update current block if provided
     if body.block_id is not None:
@@ -214,17 +238,16 @@ async def timer_action(
     await db.commit()
     await db.refresh(session)
 
-    # For 'start' events, compute elapsed from previous intervals so every
-    # client (including TV) can restore the correct offset without a cache.
+    # For 'start' and 'select' events, compute accumulated elapsed for the new
+    # block from previous intervals so every client can restore the correct offset.
     block_elapsed_seconds = 0
-    if body.event_type == "start" and event.block_id:
+    if body.event_type in ("start", "select") and event.block_id:
         tick_result = await db.execute(
             select(TimerEvent)
             .where(
                 TimerEvent.session_id == session.id,
                 TimerEvent.block_id == event.block_id,
                 TimerEvent.event_type.in_(["start", "resume", "pause"]),
-                TimerEvent.id != event.id,
             )
             .order_by(TimerEvent.occurred_at)
         )
@@ -236,6 +259,9 @@ async def timer_action(
             elif e.event_type == "pause" and last_start_time:
                 block_elapsed_seconds += int((e.occurred_at - last_start_time).total_seconds())
                 last_start_time = None
+        # For 'start' also count the current open interval
+        if body.event_type == "start" and last_start_time:
+            block_elapsed_seconds += int((datetime.utcnow() - last_start_time).total_seconds())
 
     # Broadcast the timer event to all TV clients
     ws_payload = {
@@ -244,7 +270,10 @@ async def timer_action(
         "block_id": event.block_id,
         "current_block_id": session.current_block_id,
         "is_active": session.is_active,
+        "is_paused": body.event_type == "select",
         "block_elapsed_seconds": block_elapsed_seconds,
+        "prev_block_id": prev_block_id,
+        "prev_block_elapsed_seconds": prev_block_elapsed_seconds,
     }
     await manager.broadcast(session.child_id, ws_payload)