refactor: Extract runBdCommand helper to DRY mail package (gt-8i6bg)

Extracted duplicate bd command execution pattern from mailbox.go and
router.go into a new helper function in bd.go. This reduces code
duplication and provides consistent error handling via the bdError type.

Changes:
- Added internal/mail/bd.go with runBdCommand helper and bdError type
- Refactored 5 functions in mailbox.go to use runBdCommand
- Refactored 5 functions in router.go to use runBdCommand
- Net reduction of 55 lines of code

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

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/mail/bd.go

@@ -0,0 +1,62 @@
+package mail
+
+import (
+	"bytes"
+	"os/exec"
+	"strings"
+)
+
+// bdError represents an error from running a bd command.
+// It wraps the underlying error and includes the stderr output for inspection.
+type bdError struct {
+	Err    error
+	Stderr string
+}
+
+// Error implements the error interface.
+func (e *bdError) Error() string {
+	if e.Stderr != "" {
+		return e.Stderr
+	}
+	if e.Err != nil {
+		return e.Err.Error()
+	}
+	return "unknown bd error"
+}
+
+// Unwrap returns the underlying error for errors.Is/As compatibility.
+func (e *bdError) Unwrap() error {
+	return e.Err
+}
+
+// ContainsError checks if the stderr message contains the given substring.
+func (e *bdError) ContainsError(substr string) bool {
+	return strings.Contains(e.Stderr, substr)
+}
+
+// runBdCommand executes a bd command with proper environment setup.
+// workDir is the directory to run the command in.
+// beadsDir is the BEADS_DIR environment variable value.
+// extraEnv contains additional environment variables to set (e.g., "BD_IDENTITY=...").
+// Returns stdout bytes on success, or a *bdError on failure.
+func runBdCommand(args []string, workDir, beadsDir string, extraEnv ...string) ([]byte, error) {
+	cmd := exec.Command("bd", args...) //nolint:gosec // G204: bd is a trusted internal tool
+	cmd.Dir = workDir
+
+	env := append(cmd.Environ(), "BEADS_DIR="+beadsDir)
+	env = append(env, extraEnv...)
+	cmd.Env = env
+
+	var stdout, stderr bytes.Buffer
+	cmd.Stdout = &stdout
+	cmd.Stderr = &stderr
+
+	if err := cmd.Run(); err != nil {
+		return nil, &bdError{
+			Err:    err,
+			Stderr: strings.TrimSpace(stderr.String()),
+		}
+	}
+
+	return stdout.Bytes(), nil
+}