Show current timer task in header line

(require 'org)
(require 'org-timer)
(require 'cl-lib)

(defvar my/org-timer-current-task nil)

(defun my/org-timer-start-hook ()
  (setq my/org-timer-current-task (nth 4 (org-heading-components)))
  (cl-loop for buf in (buffer-list)
           unless (string-match-p "\\`[[:space:]*]" (buffer-name buf))
           do
           (with-current-buffer buf
             (setq-local header-line-format '((" " my/org-timer-current-task " ")))))
  (setq-default header-line-format '((" " my/org-timer-current-task " "))))

(defun my/org-timer-end-hook ()
  (cl-loop for buf in (buffer-list)
           do
           (setq header-line-format nil))
  (setq-default header-line-format nil))

(dolist (hook '(org-timer-set-hook))
  (add-hook hook #'my/org-timer-start-hook))

(dolist (hook '(org-timer-done-hook org-timer-cancel-hook))
  (add-hook hook #'my/org-timer-end-hook))

Demo