fix: batch 1 audit fixes — quota SQL fixed mode, public recharge URL, WebSearch bool fallback, UpdatePlan validation

H1: incrementUsageBillingAccountQuota now uses shared dailyExpiredExpr/weeklyExpiredExpr
    constants (supporting fixed reset mode) instead of hardcoded '24 hours'/'168 hours'
H4: public settings endpoint now maps balance_low_notify_recharge_url
H6: GetWebSearchEmulationMode tolerates legacy bool values (true→enabled)
H7: UpdatePlan validates non-nil patch fields (rejects negative price, empty name, etc.)
H8: UsageTable accountBilled() helper with total_cost ?? 0 null guard
H9: AdminUsageLog TS type adds channel_id + billing_tier
M2: account.go "fixed" literals replaced with thresholdTypeFixed constant
M13: SystemSettings TS type adds web_search_emulation_enabled
UI: QuotaLimitCard title labels now use flex-1 to align with flex-1 input boxes

backend/internal/service/account_websearch_test.go

@@ -50,8 +50,8 @@ func TestGetWebSearchEmulationMode_OldBoolTrue(t *testing.T) {
 		Type:     AccountTypeAPIKey,
 		Extra:    map[string]any{featureKeyWebSearchEmulation: true},
 	}
-	// bool is not a string, type assertion fails → default
-	require.Equal(t, WebSearchModeDefault, a.GetWebSearchEmulationMode())
+	// bool true → tolerant fallback → enabled (not default)
+	require.Equal(t, WebSearchModeEnabled, a.GetWebSearchEmulationMode())
 }
 
 func TestGetWebSearchEmulationMode_OldBoolFalse(t *testing.T) {