feat(bp): /battle_pass/item_list — derives product per active season

Adds BattlePassSalesPeriodInfoDto, BattlePassProductDto, BattlePassItemListResponse DTOs,
GetItemListAsync on BattlePassService (one product if not premium + CanPurchase, empty if
already premium or off-season), and the /battle_pass/item_list controller action.
2 new integration tests; all 408 pass.

SVSim.EmulatedEntrypoint/Services/BattlePassService.cs

@@ -94,6 +94,44 @@ public sealed class BattlePassService : IBattlePassService
         };
     }
 
+    public async Task<BattlePassItemListResponse?> GetItemListAsync(long viewerId, CancellationToken ct)
+    {
+        var now = _time.GetUtcNow();
+        var season = await _bp.GetActiveSeasonAsync(now, ct);
+        if (season is null) return null;
+
+        var progress = await _viewerBp.GetOrCreateProgressAsync(viewerId, season.Id, ct);
+
+        var response = new BattlePassItemListResponse
+        {
+            PremiumPassDescription = season.Description,
+            SalesPeriodInfo = new BattlePassSalesPeriodInfoDto
+            {
+                SalesPeriodTime = FormatWireDate(season.EndDate),
+            },
+            Products = new List<BattlePassProductDto>(),
+        };
+
+        // One product per active season; empty if viewer is already premium.
+        if (!progress.IsPremium && season.CanPurchase)
+        {
+            response.Products.Add(new BattlePassProductDto
+            {
+                Id = season.Id * 1000,
+                SeasonId = season.Id,
+                Name = $"{season.Name} Premium Pass",
+                PriceCrystal = season.PriceCrystal,
+                Description = season.Description,
+                SalesPeriodInfo = new BattlePassSalesPeriodInfoDto
+                {
+                    SalesPeriodTime = FormatWireDate(season.EndDate),
+                },
+            });
+        }
+
+        return response;
+    }
+
     internal static int ComputeLevel(IReadOnlyList<BattlePassLevelEntry> curve, int point)
     {
         if (curve.Count == 0) return 1;

SVSim.EmulatedEntrypoint/Services/IBattlePassService.cs

@@ -13,4 +13,10 @@ public interface IBattlePassService
     /// (controller emits empty body in that case).
     /// </summary>
     Task<BattlePassInfoResponse?> GetInfoAsync(long viewerId, CancellationToken ct);
+
+    /// <summary>
+    /// /battle_pass/item_list payload. Returns one product per active season; empty products
+    /// array if the viewer already owns premium for the active season. Null when no active season.
+    /// </summary>
+    Task<BattlePassItemListResponse?> GetItemListAsync(long viewerId, CancellationToken ct);
 }