refactor(CS): schedule + periods are config-owned, AdminPanel-editable

Move the auto-schedule from context-owned state to the plugin config (single source
of truth): RegistrationOpenDays + RegistrationOpenTimes + Registration/Preparation/
SiegeDuration are all editable in the AdminPanel plugin config and take effect live
(context refreshes its config reference each tick via UpdateConfiguration). /csschedule
now writes the config. Removed the duplicate Persisted schedule fields. 12 tests pass.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/GameLogic/PlugIns/PeriodicTasks/CastleSiegeEventPlugIn.cs

@@ -92,7 +92,7 @@ public sealed class CastleSiegeEventPlugIn : IPeriodicTaskPlugIn, ISupportCustom
 
             // Restore state persisted before the last restart (owner/phase/registrations) BEFORE subscribing,
             // so restoring doesn't announce phases or re-spawn defenses.
-            created.RestoreState(config.PersistedOwnerGuildName, config.PersistedPhase, config.PersistedPhaseStartedUtc, config.PersistedRegisteredGuilds, config.PersistedScheduleDays, config.PersistedScheduleTime);
+            created.RestoreState(config.PersistedOwnerGuildName, config.PersistedPhase, config.PersistedPhaseStartedUtc, config.PersistedRegisteredGuilds);
 
             // Announce phase changes to the whole server and, when the siege begins, warp registered members.
             created.PhaseChanged += phase => _ = OnPhaseChangedAsync(gc, created, phase);
@@ -100,6 +100,12 @@ public sealed class CastleSiegeEventPlugIn : IPeriodicTaskPlugIn, ISupportCustom
             return created;
         });
 
+        // Point the context at the current (possibly AdminPanel-edited) config so schedule/durations are live.
+        if (this.Configuration is { } liveConfig)
+        {
+            context.UpdateConfiguration(liveConfig);
+        }
+
         await context.TickAsync(DateTime.UtcNow).ConfigureAwait(false);
 
         // During the siege, evaluate the Crown Switches (held by standing on them) and the throne capture every tick.
@@ -177,8 +183,6 @@ public sealed class CastleSiegeEventPlugIn : IPeriodicTaskPlugIn, ISupportCustom
             config.PersistedPhase = context.Phase;
             config.PersistedPhaseStartedUtc = context.PhaseStartedUtc;
             config.PersistedRegisteredGuilds = context.RegisteredGuilds.ToList();
-            config.PersistedScheduleDays = context.ScheduleDays.ToList();
-            config.PersistedScheduleTime = context.ScheduleTime;
 
             // Find our plugin-configuration row via the in-memory config graph to get its id.
             var pluginTypeId = typeof(CastleSiegeEventPlugIn).GUID;