fix: anchor Day N to each round's first game instead of lazy first sighting

The banner read "Day 1 of ~60" on day 2 of the playoffs because the old
anchor recorded whatever date we first polled a playoff game as Day 1.
Now round start dates come from /v1/schedule/playoff-series, so Day N
is authoritative and resets at each round boundary. Drops the noisy
"of ~60" denominator.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

tests/test_scheduler.py

@@ -3,10 +3,15 @@ import pytest
 from app.scheduler import start_scheduler
 
 
+def _patch_eager(mocker):
+    mocker.patch("app.scheduler.refresh_bracket")
+    mocker.patch("app.scheduler.refresh_round_start_dates")
+
+
 class TestStartScheduler:
     def test_registers_standings_refresh_every_600_seconds(self, mocker):
         mock_schedule = mocker.patch("app.scheduler.schedule")
-        mocker.patch("app.scheduler.refresh_bracket")
+        _patch_eager(mocker)
         mocker.patch("app.scheduler.time.sleep", side_effect=StopIteration)
 
         with pytest.raises(StopIteration):
@@ -17,7 +22,7 @@ class TestStartScheduler:
 
     def test_registers_score_refresh_every_10_seconds(self, mocker):
         mock_schedule = mocker.patch("app.scheduler.schedule")
-        mocker.patch("app.scheduler.refresh_bracket")
+        _patch_eager(mocker)
         mocker.patch("app.scheduler.time.sleep", side_effect=StopIteration)
 
         with pytest.raises(StopIteration):
@@ -28,7 +33,7 @@ class TestStartScheduler:
 
     def test_registers_bracket_refresh_every_3600_seconds(self, mocker):
         mock_schedule = mocker.patch("app.scheduler.schedule")
-        mocker.patch("app.scheduler.refresh_bracket")
+        _patch_eager(mocker)
         mocker.patch("app.scheduler.time.sleep", side_effect=StopIteration)
 
         with pytest.raises(StopIteration):
@@ -37,9 +42,32 @@ class TestStartScheduler:
         intervals = [call[0][0] for call in mock_schedule.every.call_args_list]
         assert 3600 in intervals
 
+    def test_registers_round_start_dates_refresh_every_21600_seconds(self, mocker):
+        mock_schedule = mocker.patch("app.scheduler.schedule")
+        _patch_eager(mocker)
+        mocker.patch("app.scheduler.time.sleep", side_effect=StopIteration)
+
+        with pytest.raises(StopIteration):
+            start_scheduler()
+
+        intervals = [call[0][0] for call in mock_schedule.every.call_args_list]
+        assert 21600 in intervals
+
     def test_invokes_bracket_refresh_eagerly_at_startup(self, mocker):
         mocker.patch("app.scheduler.schedule")
         eager = mocker.patch("app.scheduler.refresh_bracket")
+        mocker.patch("app.scheduler.refresh_round_start_dates")
+        mocker.patch("app.scheduler.time.sleep", side_effect=StopIteration)
+
+        with pytest.raises(StopIteration):
+            start_scheduler()
+
+        assert eager.called
+
+    def test_invokes_round_start_dates_refresh_eagerly_at_startup(self, mocker):
+        mocker.patch("app.scheduler.schedule")
+        mocker.patch("app.scheduler.refresh_bracket")
+        eager = mocker.patch("app.scheduler.refresh_round_start_dates")
         mocker.patch("app.scheduler.time.sleep", side_effect=StopIteration)
 
         with pytest.raises(StopIteration):
@@ -49,7 +77,7 @@ class TestStartScheduler:
 
     def test_runs_pending_on_each_tick(self, mocker):
         mock_schedule = mocker.patch("app.scheduler.schedule")
-        mocker.patch("app.scheduler.refresh_bracket")
+        _patch_eager(mocker)
         call_count = {"n": 0}
 
         def sleep_twice(_):
@@ -66,7 +94,7 @@ class TestStartScheduler:
 
     def test_continues_after_exception_in_run_pending(self, mocker):
         mock_schedule = mocker.patch("app.scheduler.schedule")
-        mocker.patch("app.scheduler.refresh_bracket")
+        _patch_eager(mocker)
         call_count = {"n": 0}
 
         def raise_then_stop(_):