feat(home): implement count for home auth dispatch requests and enable usage statistics

- Added `count` attribute to `homeAuthCount` requests to improve home message batching.
- Enabled usage statistics for home mode by default and added config-level enforcement.
- Adjusted failure logging to include detailed metadata in `UsageReporter`.
- Updated multiple executors to pass error details to `PublishFailure` for better debugging.
- Enhanced unit tests to validate `count` behavior and usage statistics enforcement across components.

internal/home/client.go

@@ -190,7 +190,20 @@ func headersToLowerMap(headers http.Header) map[string]string {
 	return out
 }
 
-func (c *Client) RPopAuth(ctx context.Context, requestedModel string, sessionID string, headers http.Header) ([]byte, error) {
+func newAuthDispatchRequest(requestedModel string, sessionID string, headers http.Header, count int) authDispatchRequest {
+	if count <= 0 {
+		count = 1
+	}
+	return authDispatchRequest{
+		Type:      "auth",
+		Model:     requestedModel,
+		Count:     count,
+		SessionID: strings.TrimSpace(sessionID),
+		Headers:   headersToLowerMap(headers),
+	}
+}
+
+func (c *Client) RPopAuth(ctx context.Context, requestedModel string, sessionID string, headers http.Header, count int) ([]byte, error) {
 	if err := c.ensureClients(); err != nil {
 		return nil, err
 	}
@@ -198,12 +211,7 @@ func (c *Client) RPopAuth(ctx context.Context, requestedModel string, sessionID
 	if requestedModel == "" {
 		return nil, fmt.Errorf("home: requested model is empty")
 	}
-	req := authDispatchRequest{
-		Type:      "auth",
-		Model:     requestedModel,
-		SessionID: strings.TrimSpace(sessionID),
-		Headers:   headersToLowerMap(headers),
-	}
+	req := newAuthDispatchRequest(requestedModel, sessionID, headers, count)
 	keyBytes, err := json.Marshal(&req)
 	if err != nil {
 		return nil, err

internal/home/client_test.go

@@ -0,0 +1,32 @@
+package home
+
+import (
+	"encoding/json"
+	"net/http"
+	"testing"
+)
+
+func TestAuthDispatchRequestIncludesCount(t *testing.T) {
+	req := newAuthDispatchRequest("gpt-5.4", "session-1", http.Header{"Authorization": {"Bearer test"}}, 2)
+
+	raw, err := json.Marshal(&req)
+	if err != nil {
+		t.Fatalf("marshal auth dispatch request: %v", err)
+	}
+
+	var payload map[string]any
+	if err := json.Unmarshal(raw, &payload); err != nil {
+		t.Fatalf("unmarshal auth dispatch request: %v", err)
+	}
+	if got := int(payload["count"].(float64)); got != 2 {
+		t.Fatalf("count = %d, want 2", got)
+	}
+}
+
+func TestAuthDispatchRequestDefaultsCountToOne(t *testing.T) {
+	req := newAuthDispatchRequest("gpt-5.4", "", nil, 0)
+
+	if req.Count != 1 {
+		t.Fatalf("count = %d, want 1", req.Count)
+	}
+}

internal/home/requests.go

@@ -3,6 +3,7 @@ package home
 type authDispatchRequest struct {
 	Type      string            `json:"type"`
 	Model     string            `json:"model"`
+	Count     int               `json:"count"`
 	SessionID string            `json:"session_id,omitempty"`
 	Headers   map[string]string `json:"headers,omitempty"`
 }