`\showStaffSwitch` at page break distorts vertical spacing

Reported as https://lists.gnu.org/archive/html/bug-lilypond/2023-12/msg00011.html.

\version "2.24.3"

<<
  { c'1 | c'1 }
  { c'1 | c'1 }
  { c'1 | c'1 }
  { c'1 | c'1 }
  { c'1 | c'1 }
  { c'1 | c'1 }
  \new Staff = "A" { c'1 | c'1 }
  \new Staff {
    c'1 | \pageBreak \showStaffSwitch
    \change Staff = "A" c'1 }
>>

Commenting out \showStaffSwitch makes it work as expected.