Show rank tier and ELO alongside RZ points in the coins badge

Adds a server-computed tier/division (Bronze..Diamond, III-I) to the
ratings profile endpoint and surfaces it next to the numeric ELO in the
shared header badge, matching the coin balance display already there.

api/QuestionsApi/Models/RatingModels.cs

@@ -47,4 +47,6 @@ public class RatingProfileResponse
     public int OverallElo { get; set; }
     public int RatedQuestionCount { get; set; }
     public Dictionary<string, int> CategoryElos { get; set; } = [];
+    public string Tier { get; set; } = "";
+    public int TierDivision { get; set; }
 }

api/QuestionsApi/Services/RatingStore.cs

@@ -27,14 +27,43 @@ public class RatingStore
     public async Task<RatingProfileResponse> GetProfileAsync(string userId)
     {
         var rating = await GetOrCreateUserRatingAsync(userId);
+        var (tierName, tierDivision) = GetTier(rating.OverallElo);
         return new RatingProfileResponse
         {
             OverallElo = rating.OverallElo,
             RatedQuestionCount = rating.RatedQuestionCount,
-            CategoryElos = rating.CategoryElos
+            CategoryElos = rating.CategoryElos,
+            Tier = tierName,
+            TierDivision = tierDivision
         };
     }
 
+    private static readonly (string Name, int FloorElo)[] TierBands =
+    [
+        ("Bronze", MinElo),
+        ("Silver", 1000),
+        ("Gold", 1300),
+        ("Platinum", 1900),
+        ("Diamond", 2200)
+    ];
+
+    private static (string Name, int Division) GetTier(int elo)
+    {
+        var bandIndex = 0;
+        for (var i = 0; i < TierBands.Length; i++)
+        {
+            if (elo >= TierBands[i].FloorElo)
+                bandIndex = i;
+        }
+
+        var band = TierBands[bandIndex];
+        var nextFloor = bandIndex + 1 < TierBands.Length ? TierBands[bandIndex + 1].FloorElo : band.FloorElo + 300;
+        var bandWidth = nextFloor - band.FloorElo;
+        var progress = bandWidth > 0 ? (elo - band.FloorElo) / (double)bandWidth : 0;
+        var division = 3 - Math.Clamp((int)(progress * 3), 0, 2);
+        return (band.Name, division);
+    }
+
     public async Task<UserRating> GetOrInitializeHistoryAsync(string userId, DateTime nowUtc)
     {
         var rating = await GetOrCreateUserRatingAsync(userId);