fix(doctor): detect missing git repo and improve daemon startup message (#890)

When not in a git repository:
- Daemon startup now shows clear message immediately instead of waiting
  5 seconds: "Note: No git repository initialized — running without
  background sync"
- Added new doctor check "Git Sync Setup" that explains the situation

Doctor check now shows three states:
1. No git repo → Warning with fix: "Run 'git init' to enable background sync"
2. Git repo, no sync-branch → OK with hint about team collaboration benefits
3. Git repo + sync-branch → OK, fully configured

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

cmd/bd/daemon_autostart_unit_test.go

@@ -8,6 +8,7 @@ import (
 	"os/exec"
 	"path/filepath"
 	"runtime"
+	"strings"
 	"testing"
 	"time"
 
@@ -280,6 +281,39 @@ func TestDaemonAutostart_StartDaemonProcess_Stubbed(t *testing.T) {
 	}
 }
 
+func TestDaemonAutostart_StartDaemonProcess_NoGitRepo(t *testing.T) {
+	// Test that startDaemonProcess returns false immediately when not in a git repo
+	tmpDir := t.TempDir()
+	oldDir, err := os.Getwd()
+	if err != nil {
+		t.Fatalf("Getwd: %v", err)
+	}
+	defer func() {
+		_ = os.Chdir(oldDir)
+	}()
+
+	// Change to a temp directory that is NOT a git repo
+	if err := os.Chdir(tmpDir); err != nil {
+		t.Fatalf("Chdir: %v", err)
+	}
+
+	// Capture stderr to verify the message
+	output := captureStderr(t, func() {
+		result := startDaemonProcess(filepath.Join(tmpDir, "bd.sock"))
+		if result {
+			t.Errorf("expected startDaemonProcess to return false when not in git repo")
+		}
+	})
+
+	// Verify the correct message is shown
+	if !strings.Contains(output, "No git repository initialized") {
+		t.Errorf("expected output to contain 'No git repository initialized', got: %q", output)
+	}
+	if !strings.Contains(output, "running without background sync") {
+		t.Errorf("expected output to contain 'running without background sync', got: %q", output)
+	}
+}
+
 func TestDaemonAutostart_RestartDaemonForVersionMismatch_Stubbed(t *testing.T) {
 	oldExec := execCommandFn
 	oldWait := waitForSocketReadinessFn