refactor: use ClientError path for logout errors in handleError

Remove manual JSON formatting for logout errors and let them fall
through to the existing ClientError branch, keeping a single point
of JSON formatting. Remove redundant Reason() method from logoutError.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: boehlke

internal/http/error.go

@@ -25,8 +25,3 @@ func (e logoutError) Error() string {
 func (e logoutError) Type() string {
 	return "logout"
 }
-
-// Reason returns the reason identifier for the client to handle logout redirection.
-func (e logoutError) Reason() string {
-	return "Logout"
-}

internal/http/http.go

@@ -537,11 +537,7 @@ func handleError(ctx context.Context, w http.ResponseWriter, err error, writeSta
 	if ctx != nil && oserror.ContextDone(err) {
 		if cause := context.Cause(ctx); cause != nil {
 			if _, isLogout := cause.(auth.LogoutError); isLogout {
-				// Send logout error message so client can redirect to login
-				logoutErr := logoutError{}
-				fmt.Fprintf(w, `{"error": {"type": "%s", "msg": "%s", "reason": "%s"}}`, logoutErr.Type(), quote(logoutErr.Error()), logoutErr.Reason())
-				fmt.Fprintln(w)
-				return
+				err = logoutError{}
 			}
 		}
 	}