refactor(server): drop stale prompt text, duplicated routes and dead options

- lib/system-prompts.ts: delete the extended prompt kept only to reach
  the 4096-token cache threshold of two old Claude models; describe the
  current canvas-first UI in the App Features section
- app/api/chat/route.ts: remove the server-side example cache (the
  browser answers examples itself), the ENABLE_HISTORY_XML_REPLACE
  option and its helper, the unread messageMetadata fields; the
  DEBUG_LLM_PAYLOAD blocks become one describeMessages summary
- app/api/log-feedback and log-save share scoreLatestTrace in
  lib/langfuse.ts
- app/api/admin/test-model and validate-model call a shared
  testModelConnection() instead of one route faking a request to the
  other and passing trust through the body
- lib/dynamo-quota-manager.ts reads the failing item from the
  conditional update instead of a second GetItem
- lib/ai-providers.ts: geminiThinkingOptions helper for the google and
  vertexai cases, drop the unused fourth resolveBaseURL parameter
- edge-functions: always stream, shrink messageSchema, drop model
  aliases nothing sends
- delete app/api/chat/xml_guide.md, parseOutputTokenLimit, unused type
  exports and export keywords on file-internal symbols
- env.example: drop variables nothing reads, document the quota,
  validation and analytics variables, mention the apiKeyEnv array form
  (also in docs/*/ai-providers.md)

docs/ja/ai-providers.md

@@ -392,7 +392,7 @@ AI_MODEL=doubao-seed-1-8-251215,doubao-seed-1-6-flash,doubao-seed-1-6-pro
 | `provider` | はい | プロバイダータイプ（`openai`, `anthropic`, `google`, `bedrock` など） |
 | `models` | はい | モデルIDのリスト |
 | `default` | いいえ | `true` に設定すると、そのプロバイダーの最初のモデルがデフォルトで選択されます |
-| `apiKeyEnv` | いいえ | カスタムAPIキー環境変数名（デフォルトは `OPENAI_API_KEY` などの標準変数） |
+| `apiKeyEnv` | いいえ | カスタムAPIキー環境変数名（デフォルトは `OPENAI_API_KEY` などの標準変数）。環境変数名の配列も指定でき、リクエストごとに値のある変数から1つがランダムに選ばれます（複数キーへの負荷分散） |
 | `baseUrlEnv` | いいえ | カスタムBase URL環境変数名 |
 
 ### 備考