feat(websearch): settings UI overhaul and quota improvements

- Remove Priority field, auto load-balance by quota remaining
- Replace QuotaRefreshInterval (daily/weekly/monthly) with SubscribedAt
  (subscription date, monthly lazy refresh via Redis TTL)
- Add collapsible provider cards, API key show/copy, usage progress bar
- Add test endpoint (POST /web-search-emulation/test) bypassing quota
- Wire WebSearchManagerBuilder on startup (was never called before)
- Fix nextMonthlyReset day-of-month overflow (Jan 31 → Feb 28)
- Fix non-deterministic sort in selectByQuotaWeight
- Map ProxyID in builder for provider-level proxy tracking
- Fix frontend timezone drift in subscribed_at date picker
- Fix provider deletion index shift for expandedProviders state

frontend/src/i18n/locales/en.ts

@@ -4417,19 +4417,24 @@ export default {
         apiKey: 'API Key',
         apiKeyPlaceholder: 'Enter API Key',
         apiKeyConfigured: 'Configured',
-        priority: 'Priority',
-        priorityHint: 'Lower number = higher priority',
+        showApiKey: 'Show',
+        hideApiKey: 'Hide',
+        copyApiKey: 'Copy',
+        copied: 'Copied',
         quotaLimit: 'Quota Limit',
         quotaLimitHint: '0 = unlimited',
-        quotaRefreshInterval: 'Refresh Interval',
-        quotaUsed: 'Used',
+        subscribedAt: 'Subscribed At',
+        subscribedAtHint: 'Quota resets monthly from this date',
+        quotaUsage: 'Usage',
         proxy: 'Proxy',
-        expiresAt: 'Expires At',
         removeProvider: 'Remove',
-        daily: 'Daily',
-        weekly: 'Weekly',
-        monthly: 'Monthly',
         noProviders: 'No search providers configured',
+        test: 'Test',
+        testDefaultQuery: 'Major world events this year',
+        testing: 'Searching...',
+        testResultTitle: 'Search Results',
+        testResultProvider: 'Provider',
+        testNoResults: 'No results found',
       },
       site: {
         title: 'Site Settings',

frontend/src/i18n/locales/zh.ts

@@ -4579,19 +4579,24 @@ export default {
         apiKey: 'API Key',
         apiKeyPlaceholder: '输入 API Key',
         apiKeyConfigured: '已配置',
-        priority: '优先级',
-        priorityHint: '数值越小优先级越高',
+        showApiKey: '显示',
+        hideApiKey: '隐藏',
+        copyApiKey: '复制',
+        copied: '已复制',
         quotaLimit: '配额上限',
         quotaLimitHint: '0 表示无限制',
-        quotaRefreshInterval: '刷新周期',
-        quotaUsed: '已使用',
+        subscribedAt: '订阅时间',
+        subscribedAtHint: '配额从此日期起每月自动重置',
+        quotaUsage: '用量',
         proxy: '代理',
-        expiresAt: '过期时间',
         removeProvider: '删除',
-        daily: '每日',
-        weekly: '每周',
-        monthly: '每月',
         noProviders: '未配置搜索服务商',
+        test: '测试',
+        testDefaultQuery: '搜索今年世界大事件',
+        testing: '搜索中...',
+        testResultTitle: '搜索结果',
+        testResultProvider: '服务商',
+        testNoResults: '无搜索结果',
       },
       site: {
         title: '站点设置',