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org-refile ​

org-refile uses org-olpath-completing-read to complete the outline path in steps, when org-refile-use-outline-path is non-nil.

Unfortunately the implementation of this Org completion table assumes that the basic completion style is used. The table is incompatible with completion styles like substring, flex or orderless. In order to fix the issue at the root, the completion table should make use of completion boundaries similar to the built-in file completion table. In your user configuration you can prioritize basic before orderless.

emacs-lisp
;; Alternative 1: Use the basic completion style
(setq org-refile-use-outline-path 'file
      org-outline-path-complete-in-steps t)

(advice-add #'org-olpath-completing-read :around #'vertico-enforce-basic-completion)

(defun vertico-enforce-basic-completion (&rest args)
  (minibuffer-with-setup-hook
      (:append
       (lambda ()
         (let ((map (make-sparse-keymap)))
           (define-key map [tab] #'minibuffer-complete)
           (use-local-map (make-composed-keymap (list map) (current-local-map))))
         (setq-local completion-styles (cons 'basic completion-styles)
                     vertico-preselect 'prompt)))
    (apply args)))

Alternatively you may want to disable the outline path completion in steps. The completion on the full path can be quicker since the input string matches directly against substrings of the full path, which is useful with Orderless. However the list of possible completions becomes much more cluttered.

emacs-lisp
;; Alternative 2: Complete full paths
(setq org-refile-use-outline-path 'file
      org-outline-path-complete-in-steps nil)