feat(usage): 修复缓存命中率计算并新增用户端 API 格式统计

- 新增 input_context_expr() 按 api_format 区分 input_tokens 语义
  (OpenAI/Gemini input_tokens 已含 cache_read，Claude 需额外加上)
- 缓存命中率统一改为基于归一化后的 total_input_context 计算
- 用户 /me/usage 接口新增 summary_by_api_format 后端聚合字段
- 前端 API 格式统计改用后端聚合数据，移除前端逐条记录手动统计
- 提取 formatHitRate 到 utils/format.ts 消除三处重复定义
- 移除 PoolManager 中未使用的 select_key 方法

Co-Authored-By: AAEE86 <ppk0227@hotmail.com>

frontend/src/api/me.ts

@@ -79,6 +79,8 @@ export interface ModelSummary {
   input_tokens: number
   output_tokens: number
   total_tokens: number
+  cache_read_tokens?: number
+  cache_hit_rate?: number
   total_cost_usd: number
   actual_total_cost_usd?: number  // 倍率消耗（仅管理员可见）
 }
@@ -88,11 +90,24 @@ export interface ProviderSummary {
   provider: string
   requests: number
   total_tokens: number
+  cache_read_tokens?: number
+  cache_hit_rate?: number
   total_cost_usd: number
   success_rate: number | null
   avg_response_time_ms: number | null
 }
 
+// API 格式统计接口
+export interface ApiFormatSummary {
+  api_format: string
+  request_count: number
+  total_tokens: number
+  cache_read_tokens: number
+  cache_hit_rate: number
+  total_cost_usd: number
+  avg_response_time_ms: number
+}
+
 // 使用统计响应接口
 export interface UsageResponse {
   total_requests: number
@@ -105,6 +120,7 @@ export interface UsageResponse {
   billing: BillingSummary
   summary_by_model: ModelSummary[]
   summary_by_provider?: ProviderSummary[]
+  summary_by_api_format?: ApiFormatSummary[]
   pagination?: {
     total: number
     limit: number

frontend/src/api/usage.ts

@@ -40,6 +40,8 @@ export interface UsageByModel {
   total_tokens: number
   total_cost: number
   avg_response_time?: number
+  cache_read_tokens?: number
+  cache_hit_rate?: number
 }
 
 export interface UsageByUser {
@@ -61,6 +63,8 @@ export interface UsageByProvider {
   avg_response_time_ms: number
   success_rate: number
   error_count: number
+  cache_read_tokens?: number
+  cache_hit_rate?: number
 }
 
 export interface UsageByApiFormat {
@@ -70,6 +74,8 @@ export interface UsageByApiFormat {
   total_cost: number
   actual_cost: number
   avg_response_time_ms: number
+  cache_read_tokens?: number
+  cache_hit_rate?: number
 }
 
 export interface UsageFilters {