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/Program.cs

@@ -45,6 +45,9 @@ builder.Services.AddHttpClient<GerbilManagerWebAPI.SaleAd.SaleAdService>(
 // INBOX-2: KI-Antwortentwurf (gleiche AI-Sektion, gleicher Wire-Client).
 builder.Services.AddHttpClient<GerbilManagerWebAPI.Inbox.DraftReplyService>(
     http => http.Timeout = TimeSpan.FromSeconds(60));
+// FEAT-NAMEGEN: Name suggestions via Gemini (same AI section, same wire client).
+builder.Services.AddHttpClient<GerbilManagerWebAPI.Names.NameSuggestionService>(
+    http => http.Timeout = TimeSpan.FromSeconds(60));
 
 // INBOX-0: Gmail inbox. App Password encrypted at rest via Data Protection.
 // AR-3: persist the key ring so encrypted passwords survive image redeployments.
@@ -100,6 +103,7 @@ app.MapSettingsEndpoints();
 app.MapExportEndpoints();
 app.MapCmsEndpoints();
 app.MapRequestEndpoints();
+app.MapNamesEndpoints();
 
 app.Run();