\version "2.22"

prebreakmarkup = \markup\musicglyph "scripts.segno"
postbreakmarkup = \markup\musicglyph "scripts.coda"

#(define (marksplitcallback grob)
  (let ((status (ly:item-break-dir grob)))
       (cond ((< status 0) ; broken end
              (ly:grob-set-property! grob 'text prebreakmarkup)
              (ly:grob-set-property! grob 'stencil (ly:text-interface::print grob)))
             ((> status 0) ; broken start
              (ly:grob-set-property! grob 'text postbreakmarkup)
              (ly:grob-set-property! grob 'stencil (ly:text-interface::print grob))))))

{
   g'2 8 4.
   \once\override Score.RehearsalMark.after-line-breaking = #marksplitcallback
   \once\override Score.RehearsalMark.break-visibility = #all-visible
   \mark \markup {
     \musicglyph "scripts.segno"
     \musicglyph "scripts.coda"
   } \break
   b'2 r |
   g'2 8 4.
   \once\override Score.RehearsalMark.after-line-breaking = #marksplitcallback
   \once\override Score.RehearsalMark.break-visibility = #all-visible
   \mark \markup {
     \musicglyph "scripts.segno"
     \musicglyph "scripts.coda"
   }
   b'2
}