FEAT-NAMEGEN: GET /names/suggest backend (Gemini, 503 NamesKeyMissing, LitterLetter)

- NameSuggestionService: Gemini via existing OpenAiChatClient, builds
  letter/gender/usages/count prompt, strips markdown fences from response,
  deserialises [{name,meaning,origin}] array; NotConfigured -> 503.
- GET /names/suggest?letter=&gender=&usages=&count= -> Ok<List<NameSuggestion>>
  | 503 {code:NamesKeyMissing} | 502 {code:NamesUpstreamError}.
- Litter.LitterLetter (string?, nullable) + AddLitterLetter migration.
- 17 new tests (prompt assembly, fence strip, parse edge cases,
  503-not-configured, upstream-error); total 157/157 green.
- No Behind-the-Name dependency — Gemini path only (Julian's decision).

Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>

GerbilManagerWebAPI/Endpoints/NamesEndpoints.cs

@@ -0,0 +1,38 @@
+using GerbilManagerWebAPI.Names;
+
+namespace GerbilManagerWebAPI.Endpoints
+{
+    /// <summary>
+    /// FEAT-NAMEGEN: GET /names/suggest — meaningful gerbil name suggestions via Gemini.
+    ///
+    /// 503 {code:"NamesKeyMissing"} while the AI section is unconfigured — the
+    /// frontend maps exactly this code to its German disabled-state hint.
+    /// </summary>
+    public static class NamesEndpoints
+    {
+        public static IEndpointRouteBuilder MapNamesEndpoints(this IEndpointRouteBuilder app)
+        {
+            app.MapGet("/names/suggest", async (
+                string? letter,
+                string? gender,
+                string? usages,
+                int count,
+                NameSuggestionService service,
+                CancellationToken ct) =>
+            {
+                var result = await service.SuggestAsync(letter, gender, usages, count, ct);
+                return result.Status switch
+                {
+                    NameSuggestionStatus.Ok => Results.Ok(result.Suggestions),
+                    NameSuggestionStatus.NotConfigured => Results.Json(
+                        new { code = "NamesKeyMissing", message = result.Error ?? "" }, statusCode: 503),
+                    _ => Results.Json(
+                        new { code = "NamesUpstreamError", message = result.Error ?? "" }, statusCode: 502),
+                };
+            })
+            .WithTags("Names");
+
+            return app;
+        }
+    }
+}