test: add unit tests for billing, websearch, and notify systems

Billing (25 tests):
- CalculateCostUnified: nil resolver fallback, token/per_request/image modes
- GetModelPricingWithChannel: nil/partial/full channel overrides
- resolveAccountStatsCost: four-level priority chain integration tests

WebSearch (18 tests):
- PopulateWebSearchUsage: nil input, manager states, QuotaLimit nil/*int64
- ResetWebSearchUsage: nil manager error
- Manager.ResetUsage: nil Redis
- shouldEmulateWebSearch: full decision chain (8 scenarios)

Notify (36 tests):
- ParseNotifyEmails/MarshalNotifyEmails: old/new format, roundtrip
- crossedDownward: boundary values, threshold semantics
- checkQuotaDimCrossings: mixed dimensions, disabled/zero skip

backend/internal/pkg/websearch/manager_test.go

@@ -313,3 +313,11 @@ func TestNewHTTPClient_ValidSOCKS5Proxy(t *testing.T) {
 	require.NoError(t, err)
 	require.NotNil(t, c)
 }
+
+// --- ResetUsage ---
+
+func TestManager_ResetUsage_NilRedis(t *testing.T) {
+	m := NewManager(nil, nil)
+	err := m.ResetUsage(context.Background(), "brave")
+	require.NoError(t, err)
+}