fix: hide score on submit + total denominator + projector chart cleanup

Three small UX/fairness tweaks from manual live testing:

1. Post-submit "wait for reveal" screen: show only the response time, no
   score. The +score reveal leaked correctness — any positive number =
   correct, zero = wrong — short-circuiting the "stop and think" beat
   the reveal pause was supposed to enforce. Time stays as the
   engagement signal; score now waits for the instructor reveal.

2. Final-screen "Correct X / Y" denominator is now total_questions
   instead of questions_answered. Missed questions are scored zero, so
   they belong in the denominator visibly. Server adds total_questions
   to the session_ended payload.

3. Projector score-distribution: drop the in-chart count labels (they
   collided with each other and with the median tag at small N), restore
   the previously-computed-but-not-rendered x-axis tick labels at the
   bottom. Stats line at the foot keeps n / mean / max.

Also: short-circuit the per-submit instructor + presence broadcasts
when no instructor / projector is connected (no listener, no DB work).
The 50-student load test was tight on margin against its 2 s
time_limit; with the new presence_message / live_histogram_message DB
queries firing on every submit, the margin disappeared on busy boxes.
Conftest fixture also bumped to 8 s per question for the same reason —
gives breathing room for sequential WS submits in the load test.

71/71 pytest green.

app/room.py

@@ -586,7 +586,11 @@ class RoomManager:
                     (sid, student_id, qidx, stored_answer, submitted_at, elapsed_ms, score),
                 )
                 await db.commit()
-        await self.broadcast_instructors(sid, await self.live_histogram_message(sid, qidx))
+        # Skip live histogram build when there's no instructor listening
+        # — same rationale as broadcast_presence. Submit storm should not
+        # be paying for DB work that nobody consumes.
+        if self.instructor_clients.get(sid):
+            await self.broadcast_instructors(sid, await self.live_histogram_message(sid, qidx))
         await self.broadcast_presence(sid)
         await self.broadcast_projectors(sid)
         return {"type": "submit_ack", "question_idx": qidx, "answer": stored_answer, "score": score, "elapsed_ms": elapsed_ms}
@@ -719,7 +723,16 @@ class RoomManager:
 
     async def ended_message(self, sid: str, identity: dict[str, Any] | None = None) -> dict[str, Any]:
         you_id = identity["student_id"] if identity else None
-        msg = {"type": "session_ended", "final_top5": await self.leaderboard(sid, limit=5, you_student_id=you_id)}
+        pool = await self.get_pool_for_session(sid)
+        msg = {
+            "type": "session_ended",
+            "final_top5": await self.leaderboard(sid, limit=5, you_student_id=you_id),
+            # Total questions in the pool — clients use this as the
+            # denominator on the "Correct X / Y" display so missed
+            # questions are visibly counted as wrong (X stays low),
+            # rather than hiding behind a smaller denominator.
+            "total_questions": question_count(pool),
+        }
         if identity:
             student = identity["student_id"]
             msg.update(await self.student_summary(sid, student))
@@ -941,6 +954,14 @@ class RoomManager:
         }
 
     async def broadcast_presence(self, sid: str) -> None:
+        # Skip the (DB-heavy) message build when no instructor is listening.
+        # The presence_message touches participants + question_events +
+        # student_events + submissions; on a 50-student submit storm
+        # those queries ran for every submit even if no admin was on
+        # the WS, eating budget that mattered to the time-limited
+        # question close.
+        if not self.instructor_clients.get(sid):
+            return
         await self.broadcast_instructors(sid, await self.presence_message(sid))
 
     # ---- Projector (public big-screen view) -------------------------------