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/cn/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` | 是 | 提供商类型（`openai`, `anthropic`, `google`, `bedrock` 等） |
 | `models` | 是 | 模型 ID 列表 |
 | `default` | 否 | 设为 `true` 表示默认选中该提供商的第一个模型 |
-| `apiKeyEnv` | 否 | 自定义 API Key 环境变量名（默认使用提供商标准变量如 `OPENAI_API_KEY`） |
+| `apiKeyEnv` | 否 | 自定义 API Key 环境变量名（默认使用提供商标准变量如 `OPENAI_API_KEY`）。也可以写成环境变量名数组，每次请求从有值的变量中随机选一个，把负载分摊到多个 Key 上 |
 | `baseUrlEnv` | 否 | 自定义 Base URL 环境变量名 |
 
 ### 说明

docs/en/ai-providers.md

@@ -407,7 +407,7 @@ This is shorthand for the equivalent `ai-models.json`. For multiple providers or
 | `provider` | Yes | Provider type (`openai`, `anthropic`, `google`, `bedrock`, etc.) |
 | `models` | Yes | List of model IDs |
 | `default` | No | Set to `true` to auto-select this provider's first model as default |
-| `apiKeyEnv` | No | Custom API key env var name (defaults to provider's standard var like `OPENAI_API_KEY`) |
+| `apiKeyEnv` | No | Custom API key env var name (defaults to provider's standard var like `OPENAI_API_KEY`). May also be an array of env var names: each request picks one that has a value at random, spreading load over several keys |
 | `baseUrlEnv` | No | Custom base URL env var name |
 
 ### Notes

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