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

backend/internal/server/routes/admin.go

@@ -410,6 +410,7 @@ func registerSettingsRoutes(admin *gin.RouterGroup, h *handler.Handlers) {
 		// Web Search 模拟配置
 		adminSettings.GET("/web-search-emulation", h.Admin.Setting.GetWebSearchEmulationConfig)
 		adminSettings.PUT("/web-search-emulation", h.Admin.Setting.UpdateWebSearchEmulationConfig)
+		adminSettings.POST("/web-search-emulation/test", h.Admin.Setting.TestWebSearchEmulation)
 	}
 }