Vertically aligned StaffGroups without connecting SystemStartBar

This snippet shows how to achieve vertically aligned StaffGroups with a SystemStartBar for each StaffGroup, but without connecting them.

Note that this only works properly for music that can be printed as a single system.

\version "2.24"

#(set-global-staff-size 15)

\paper {
  ragged-right = ##f
  print-all-headers = ##t
  tagline = ##f
}

\layout {
  \context {
    \StaffGroup
    \consists Text_mark_engraver
    \consists Staff_collecting_engraver
    systemStartDelimiterHierarchy =
      #'(SystemStartBrace (SystemStartBracket a b))
  }

  \context {
    \Score
    \remove Text_mark_engraver
    \remove Staff_collecting_engraver
    \override SystemStartBrace.style = #'bar-line
    \omit SystemStartBar
    \override SystemStartBrace.padding = #-0.1
    \override SystemStartBrace.thickness = #1.6
    \override StaffGrouper.staffgroup-staff-spacing.basic-distance = #15
  }
}

%%%% EXAMPLE

txt =
\lyricmode {
  Wer4 nur den lie -- ben Gott läßt wal2 -- ten4
  und4 hof -- fet auf ihn al -- le Zeit2.
}

% First StaffGroup "exercise"

eI = \relative c' {
  \textMark \markup {
    \bold Teacher:
    This is a simple setting of the choral. Please improve it. }
  \key a \minor
  \time 4/4
  \voiceOne
  
  \partial 4 e4
  a b c b
  a b gis2
  e4\fermata g! g f
  e a a gis
  a2.\fermata
  \bar ":|."
}

eII = \relative c' {
  \key a \minor
  \time 4/4
  \voiceTwo
  \partial 4 c4
  e e e gis
  a f e2
  b4 b d d
  c c d d
  c2.
  \bar ":|."
}

eIII = \relative c' {
  \key a \minor
  \time 4/4
  \clef bass
  \voiceOne
  
  \partial 4 a4
  c b a b
  c d b2
  gis4 g g b
  c a f e
  e2.
}

eIV = \relative c' {
  \key a \minor
  \time 4/4
  \clef bass
  \voiceTwo
  
  \partial 4 a,4
  a' gis a e
  a, d e2
  e,4\fermata e' b g
  c f d e
  a,2.\fermata
  \bar ":|."
}

exercise = \new StaffGroup = "exercise" <<
  \new Staff <<
    \new Voice \eI
    \new Voice \eII
  >>

  \new Lyrics \txt

  \new Staff <<
    \new Voice \eIII
    \new Voice \eIV
  >>
>>


% Second StaffGroup "simple Bach"

sbI = \relative c' {
  \textMark \markup { \bold" Pupil:" Here's my version! }
  \key a \minor
  \time 4/4
  \voiceOne
  
  \partial 4 e4
  a b c b
  a b gis2
  e4\fermata g! g f
  e a a gis
  a2.\fermata
  \bar ":|."
}

sbII = \relative c' {
  \key a \minor
  \time 4/4
  \voiceTwo
  \partial 4 c8 d
  e4 e e8 f g4
  f f e2
  b4 b8 c d4 d
  e8 d c4 b8 c d4
  c2.
  \bar ":|."
}

sbIII = \relative c' {
  \key a \minor
  \time 4/4
  \clef bass
  \voiceOne
  
  \partial 4 a8 b
  c4 b a b8 c
  d4 d8 c b2
  gis4 g g8 a b4
  b a8 g f4 e
  e2.
}

sbIV = \relative c' {
  \key a \minor
  \time 4/4
  \clef bass
  \voiceTwo
  
  \partial 4 a,4
  a' gis a e
  f8 e d4 e2
  e,4\fermata e' b a8 g
  c4 f8 e d4 e
  a,2.\fermata
  \bar ":|."
}

simpleBach = \new StaffGroup = "simple Bach" <<
  \new Staff <<
    \new Voice \sbI
    \new Voice \sbII
  >>

  \new Lyrics \txt

  \new Staff <<
    \new Voice \sbIII
    \new Voice \sbIV
  >>
>>


% Third StaffGroup "chromatic Bach"

cbI = \relative c' {
  \textMark \markup {
    \bold "Teacher:"
    \column {
      "Well, you simply copied and transposed a version of J.S.Bach."
      "Do you know this one?"
    }
  }
  \key a \minor
  \time 4/4
  \voiceOne
  
  \partial 4 e4
  a b c b
  a b gis4. fis8
  e4\fermata g! g f
  e a a8 b gis4
  a2.\fermata
  \bar ":|."
}

cbII = \relative c' {
  \key a \minor
  \time 4/4
  \voiceTwo

  \partial 4 c8 d
  e4 e e8 fis gis4
  a8 g! f!4 e2
  b4 e e d
  d8[ cis] d dis e fis e4
  e2.
  \bar ":|."
}

cbIII = \relative c' {
  \key a \minor
  \time 4/4
  \clef bass
  \voiceOne
  
  \partial 4 a8 b
  c[ b] a gis8 a4 d,
  e8[ e'] d c b4. a8
  gis4 b c d8 c
  b[ a] a b c b b c16 d
  c2.
}

cbIV = \relative c' {
  \key a \minor
  \time 4/4
  \clef bass
  \voiceTwo
  
  \partial 4 a4
  c, e a, b
  c d e2
  e4\fermata e a b8 c
  gis[ g] fis f e dis e4
  a,2.\fermata
  \bar ":|."
}

chromaticBach = \new StaffGroup = "chromatic Bach" <<
  \new Staff <<
    \new Voice \cbI
    \new Voice \cbII
  >>

  \new Lyrics \txt

  \new Staff <<
    \new Voice \cbIII
    \new Voice \cbIV
  >>
>>


% Score

\score {
  <<
    \exercise
    \simpleBach
    \chromaticBach
  >>
  
  \header {
    title = \markup \column {
              \combine \null \vspace #1
              "Exercise: Improve the given choral"
              " "
            }
  }

  \layout {
    \context {
      \Lyrics
      \override LyricText.X-offset = #-1
    }
  }
}