feat(CS): persist owner/phase/registrations across restarts via plugin config JSON

Castle Siege state was in-memory, so the castle owner (and thus the P4 hunting-map
reward) reset on every server restart/redeploy. Now the context marks itself dirty
on any persistable change (phase transition, registration, owner set); the plugin's
periodic tick writes a snapshot into its own PlugInConfiguration CustomConfiguration
(a JSON blob already stored in PostgreSQL - no schema migration) and restores it on
startup. Battle state (defenses/switches/occupier) stays transient. +2 unit tests.

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

src/GameLogic/CastleSiege/CastleSiegeConfiguration.cs

@@ -31,6 +31,23 @@ public class CastleSiegeConfiguration
     /// </summary>
     public int RegistrationFee { get; set; } = 100000;
 
+    // --- Persisted runtime state (P4 persistence) ---
+    // These ride on the plugin's custom-configuration JSON (already stored in PostgreSQL), so the castle
+    // owner and the current cycle survive server restarts without a dedicated database table/migration.
+    // Written by CastleSiegeEventPlugIn whenever the state changes; read back on startup to restore it.
+
+    /// <summary>Gets or sets the persisted castle owner guild name (null = unowned).</summary>
+    public string? PersistedOwnerGuildName { get; set; }
+
+    /// <summary>Gets or sets the persisted current phase, so the cycle resumes after a restart.</summary>
+    public CastleSiegePhase PersistedPhase { get; set; } = CastleSiegePhase.Ownership;
+
+    /// <summary>Gets or sets when the persisted phase started (UTC), or null if never persisted.</summary>
+    public DateTime? PersistedPhaseStartedUtc { get; set; }
+
+    /// <summary>Gets or sets the persisted registered guild names for the current cycle.</summary>
+    public IList<string> PersistedRegisteredGuilds { get; set; } = new List<string>();
+
     /// <summary>
     /// Returns true if <paramref name="now"/> falls within a 5-second window of any configured
     /// registration-open time.