fix: auto-create default branch on cafe registration + backfill existing

- VerifyRegisterAsync: create a Branch named after the café alongside
  the Café and Owner, so new owners can use the dashboard immediately
  without hitting the "select a branch" gate
- PlatformDataSeeder: EnsureDefaultBranchesAsync runs on every boot and
  creates a default branch for any existing café that has none (covers
  cafés registered before this fix)

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

src/Meezi.API/Services/AuthService.cs

@@ -367,6 +367,15 @@ public class AuthService : IAuthService
             PlanTier = PlanTier.Free,
         };
 
+        // Auto-create a default main branch so the owner can start using the
+        // dashboard immediately without hitting the "select a branch" gate.
+        var defaultBranch = new Branch
+        {
+            CafeId   = cafe.Id,
+            Name     = cafeName,
+            IsActive = true,
+        };
+
         var owner = new Employee
         {
             CafeId = cafe.Id,
@@ -376,6 +385,7 @@ public class AuthService : IAuthService
         };
 
         _db.Cafes.Add(cafe);
+        _db.Branches.Add(defaultBranch);
         _db.Employees.Add(owner);
         await _db.SaveChangesAsync(cancellationToken);
 

src/Meezi.Infrastructure/Data/PlatformDataSeeder.cs

@@ -125,8 +125,46 @@ public static class PlatformDataSeeder
         await EnsureCatalogUpgradesAsync(db, logger);
     }
 
+    /// <summary>
+    /// Ensures every café has at least one active branch. Idempotent.
+    /// Creates a default branch named after the café for any café that has none.
+    /// </summary>
+    private static async Task EnsureDefaultBranchesAsync(AppDbContext db, ILogger logger)
+    {
+        // Load café IDs that have zero branches in one query
+        var cafeIdsWithBranches = await db.Branches
+            .Where(b => b.DeletedAt == null)
+            .Select(b => b.CafeId)
+            .Distinct()
+            .ToListAsync();
+
+        var cafesWithoutBranch = await db.Cafes
+            .Where(c => c.DeletedAt == null && !cafeIdsWithBranches.Contains(c.Id))
+            .Select(c => new { c.Id, c.Name })
+            .ToListAsync();
+
+        if (cafesWithoutBranch.Count == 0) return;
+
+        foreach (var cafe in cafesWithoutBranch)
+        {
+            db.Branches.Add(new Branch
+            {
+                CafeId   = cafe.Id,
+                Name     = cafe.Name,
+                IsActive = true,
+            });
+        }
+
+        await db.SaveChangesAsync();
+        logger.LogInformation("Created default branch for {Count} café(s) that had none", cafesWithoutBranch.Count);
+    }
+
     private static async Task EnsureCatalogUpgradesAsync(AppDbContext db, ILogger logger)
     {
+        // Ensure every café has at least one branch. Cafés registered before the
+        // auto-branch feature was added are patched on the first boot after upgrade.
+        await EnsureDefaultBranchesAsync(db, logger);
+
         var featureAdds = new[]
         {
             ("menu_3d", "منوی سه‌بعدی", "3D menu", "growth"),