I also need a ready-made function for retrieving the regexp for symbol
at point.

I can install this as a new defun in subr.el

    (defun find-tag-default-as-regexp ()
      (let* ((tagf (or find-tag-default-function
                       (get major-mode 'find-tag-default-function)
                       'find-tag-default))
             (tag (funcall tagf)))
        (cond ((not tag))
              ((eq tagf 'find-tag-default)
               (format "\\_<%s\\_>" (regexp-quote tag)))
              (t (regexp-quote tag)))))

or

Augment existing `find-tag-default' to take an optional argument like so