\version "2.22"

connectArrowStem =
#(define-music-function (dir) (ly:dir?)
    #{
      \once {
        \undo \omit Stem % in case someone \omit'ted them 
        \override Stem.length-fraction = 0
        \override Stem.X-offset = 0.65
        \override Stem.thickness = 2
        \override Stem.stencil =
        #(grob-transformer
          'stencil
          (lambda (grob stem)
            (let* ((Y-ext (ly:stencil-extent stem Y))
                   (Y-pos (interval-index Y-ext (* dir 0.3))))
              (ly:stencil-add
               stem
               (ly:stencil-translate-axis
                (parenthesize-stencil (grob-interpret-markup grob (markup #:arrow-head Y dir #f)) 0.08 0.25 0.4 0.07)
                Y-pos Y)))))
      }
    #})

{
   \omit Stem
   c'4 d' e'4
   \connectArrowStem #UP <c' g''>4
   \connectArrowStem #DOWN <b' g''>
}