refactor: 搬入 errorUtils 并迁移消费者导入到 model-provider

- 搬入 formatAPIError、extractConnectionErrorDetails 等 errorUtils
- 迁移 10 个消费者文件直接从 @anthropic-ai/model-provider 导入
- 更新 emptyUsage、sdkUtilityTypes、systemPromptType 为 re-export proxy

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/utils/sideQuestion.ts

@@ -6,8 +6,8 @@
  * while keeping the side question response separate from main conversation.
  */
 
-import { formatAPIError } from '../services/api/errorUtils.js'
-import type { NonNullableUsage } from '../services/api/logging.js'
+import { formatAPIError } from '@anthropic-ai/model-provider'
+import type { NonNullableUsage } from '@anthropic-ai/model-provider'
 import type { Message, SystemAPIErrorMessage } from '../types/message.js'
 import { type CacheSafeParams, runForkedAgent } from './forkedAgent.js'
 import { createUserMessage, extractTextContent } from './messages.js'