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/service/websearch_config.go

@@ -22,15 +22,14 @@ type WebSearchEmulationConfig struct {
 
 // WebSearchProviderConfig describes a single search provider (Brave or Tavily).
 type WebSearchProviderConfig struct {
-	Type                 string `json:"type"`                   // websearch.ProviderTypeBrave | Tavily
-	APIKey               string `json:"api_key,omitempty"`      // secret — omitted in API responses
-	APIKeyConfigured     bool   `json:"api_key_configured"`     // read-only mask
-	Priority             int    `json:"priority"`               // lower = higher priority
-	QuotaLimit           int64  `json:"quota_limit"`            // 0 = unlimited
-	QuotaRefreshInterval string `json:"quota_refresh_interval"` // websearch.QuotaRefresh*
-	QuotaUsed            int64  `json:"quota_used,omitempty"`   // read-only: current period usage
-	ProxyID              *int64 `json:"proxy_id"`               // optional proxy association
-	ExpiresAt            *int64 `json:"expires_at,omitempty"`   // optional expiration timestamp
+	Type             string `json:"type"`                    // websearch.ProviderTypeBrave | Tavily
+	APIKey           string `json:"api_key,omitempty"`       // secret — omitted in API responses
+	APIKeyConfigured bool   `json:"api_key_configured"`      // read-only mask
+	QuotaLimit       int64  `json:"quota_limit"`             // 0 = unlimited
+	SubscribedAt     *int64 `json:"subscribed_at,omitempty"` // subscription start (unix seconds); quota resets monthly
+	QuotaUsed        int64  `json:"quota_used,omitempty"`    // read-only: current usage from Redis
+	ProxyID          *int64 `json:"proxy_id"`                // optional proxy association
+	ExpiresAt        *int64 `json:"expires_at,omitempty"`    // optional expiration timestamp
 }
 
 // --- Validation ---
@@ -42,13 +41,6 @@ var validProviderTypes = map[string]bool{
 	websearch.ProviderTypeTavily: true,
 }
 
-var validQuotaIntervals = map[string]bool{
-	websearch.QuotaRefreshDaily:   true,
-	websearch.QuotaRefreshWeekly:  true,
-	websearch.QuotaRefreshMonthly: true,
-	"":                            true, // defaults to monthly
-}
-
 func validateWebSearchConfig(cfg *WebSearchEmulationConfig) error {
 	if cfg == nil {
 		return nil
@@ -61,9 +53,6 @@ func validateWebSearchConfig(cfg *WebSearchEmulationConfig) error {
 		if !validProviderTypes[p.Type] {
 			return fmt.Errorf("provider[%d]: invalid type %q", i, p.Type)
 		}
-		if !validQuotaIntervals[p.QuotaRefreshInterval] {
-			return fmt.Errorf("provider[%d]: invalid quota_refresh_interval %q", i, p.QuotaRefreshInterval)
-		}
 		if p.QuotaLimit < 0 {
 			return fmt.Errorf("provider[%d]: quota_limit must be >= 0", i)
 		}
@@ -237,17 +226,55 @@ func (s *SettingService) RebuildWebSearchManager(ctx context.Context) {
 	slog.Info("websearch: manager rebuilt", "provider_count", len(providerConfigs))
 }
 
-// SanitizeWebSearchConfig returns a copy with api_key fields masked for API responses.
-func SanitizeWebSearchConfig(cfg *WebSearchEmulationConfig) *WebSearchEmulationConfig {
+// WebSearchTestResult holds the result of a search test.
+type WebSearchTestResult struct {
+	Provider string                   `json:"provider"`
+	Results  []websearch.SearchResult `json:"results"`
+	Query    string                   `json:"query"`
+}
+
+// TestWebSearch executes a test search using the currently configured Manager.
+// Uses Manager.TestSearch which bypasses quota tracking.
+func TestWebSearch(ctx context.Context, query string) (*WebSearchTestResult, error) {
+	mgr := getWebSearchManager()
+	if mgr == nil {
+		return nil, fmt.Errorf("web search: manager not initialized, save config first")
+	}
+	resp, providerName, err := mgr.TestSearch(ctx, websearch.SearchRequest{
+		Query:      query,
+		MaxResults: webSearchDefaultMaxResults,
+	})
+	if err != nil {
+		return nil, err
+	}
+	return &WebSearchTestResult{
+		Provider: providerName,
+		Results:  resp.Results,
+		Query:    resp.Query,
+	}, nil
+}
+
+// SanitizeWebSearchConfig returns a copy with api_key fields masked and quota usage populated.
+func SanitizeWebSearchConfig(ctx context.Context, cfg *WebSearchEmulationConfig) *WebSearchEmulationConfig {
 	if cfg == nil {
 		return nil
 	}
 	out := *cfg
 	out.Providers = make([]WebSearchProviderConfig, len(cfg.Providers))
+
+	// Load usage from the global Manager (reads from Redis)
+	mgr := getWebSearchManager()
+
 	for i, p := range cfg.Providers {
 		out.Providers[i] = p
 		out.Providers[i].APIKeyConfigured = p.APIKey != ""
 		out.Providers[i].APIKey = "" // never return the secret
+
+		// Populate quota usage from Redis
+		if mgr != nil {
+			used, _ := mgr.GetUsage(ctx, p.Type)
+			out.Providers[i].QuotaUsed = used
+		}
 	}
 	return &out
 }