\version "2.22.1"


#(define (my-callback grob)
  (let* (
         ; have we been split?
         (orig (ly:grob-original grob))
         ; if yes, get the split pieces (our siblings)
         (siblings (if (ly:grob? orig)
                     (ly:spanner-broken-into orig) '() )))
   (if (and (>= (length siblings) 2)
             (not (eq? (car siblings) grob)))
     (ly:grob-set-property! grob 'text #f)
     (ly:grob-set-property! grob 'stencil (ly:ottava-bracket::print grob)))))

\score {

\new Staff {
\set Staff.ottavationMarkups = #ottavation-ordinals
\override Staff.OttavaBracket.after-line-breaking = #my-callback
  \ottava #1
 c''' 4 d''' e'''' f''''
 \break
 d''' f'''' g'''' a''''
 \break
 d''' f''' g''' a'''

   }
}