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Assuming GNU gawk ... No fault proofing included though(Taking your word for: "that is the literal document") ... So,:

$ cat file
foo
foobar
  bar
  baz
    bat
bar
$
$ gawk 'BEGIN {
    PROCINFO["sorted_in"] = "@ind_str_asc"
}

{
    match($0, /^[ \t]*/)
    if (RLENGTH == 0) {
        if (NR > 1 && length(a) == 1) {
            print a[0]
        }
        delete a
        a[0] = $0
        lsnum = RLENGTH
    }
    if (RLENGTH > lsnum) {
        lsnum = RLENGTH
        a[lsnum] = "." substr($0, RLENGTH + 1)
        p = 1
    }
    if (p == 1) {
        for (i in a) {
            printf "%s", a[i]
        }
        print ""
        lsnum = 0
        p = 0
    }
}

END {
    if (length(a) == 1) {
        print a[0]
    }
}' file
foo
foobar.bar
foobar.baz
foobar.baz.bat
bar

Assuming GNU gawk ... No fault proofing included though(Taking your word for: "that is the literal document") ... So,:

$ cat file
foo
foobar
  bar
  baz
    bat
bar
$
$ gawk 'BEGIN {
    PROCINFO["sorted_in"] = "@ind_num_asc"
}

{
    match($0, /^[ \t]*/)
    if (RLENGTH == 0) {
        if (NR > 1 && length(a) == 1) {
            print a[0]
        }
        delete a
        a[0] = $0
        lsnum = RLENGTH
    }
    if (RLENGTH > lsnum) {
        lsnum = RLENGTH
        a[lsnum] = "." substr($0, RLENGTH + 1)
        p = 1
    }
    if (p == 1) {
        for (i in a) {
            printf "%s", a[i]
        }
        print ""
        lsnum = 0
        p = 0
    }
}

END {
    if (length(a) == 1) {
        print a[0]
    }
}' file
foo
foobar.bar
foobar.baz
foobar.baz.bat
bar

That should work if the lines in your file are preceded with either spaces or tabs … However, for a mix of the two, you might need to tweak a bit to e.g. parse tabs into spaces or vice versa to avoid duplicate indices which will set the wrong array elements and result in faulty output.

$ cat doc
foo
foobar
  bar
  baz
    bat
bar
$
$ gawk '{
   match($0, /^[ \t]*/);
   if ( RLENGTH == 0 ) {
   if ( NR > 1 && length(a) == 1 ) {
   print a[0] }
   delete a;
   a[0] = $0;
   lsnum = RLENGTH}
   if ( RLENGTH > lsnum ) {
   lsnum = RLENGTH;
   a[lsnum] = "."substr($0,RLENGTH+1);
   p = 1}
   if ( RLENGTH == lsnum && p == 1 ) {
   for (i in a) {
   printf "%s", a[i] }
   print ""; lsnum = 0; p = 0} } END {
   if ( NR > 1 && length(a) == 1 ) {
   print a[0] } }' doc
foo
foobar.bar
foobar.baz
foobar.baz.bat
bar

EDIT: here is the above script formatted by gawk -o- for readability:

{
        match($0, /^[ \t]*/)
        if (RLENGTH == 0) {
                if (NR > 1 && length(a) == 1) {
                        print a[0]
                }
                delete a
                a[0] = $0
                lsnum = RLENGTH
        }
        if (RLENGTH > lsnum) {
                lsnum = RLENGTH
                a[lsnum] = "." substr($0, RLENGTH + 1)
                p = 1
        }
        if (RLENGTH == lsnum && p == 1) {
                for (i in a) {
                        printf "%s", a[i]
                }
                print ""
                lsnum = 0
                p = 0
        }
}

END {
        if (NR > 1 && length(a) == 1) {
                print a[0]
        }
}

$ cat file
foo
foobar
  bar
  baz
    bat
bar
$
$ gawk 'BEGIN {
    PROCINFO["sorted_in"] = "@ind_str_asc"
}

{
    match($0, /^[ \t]*/)
    if (RLENGTH == 0) {
        if (NR > 1 && length(a) == 1) {
            print a[0]
        }
        delete a
        a[0] = $0
        lsnum = RLENGTH
    }
    if (RLENGTH > lsnum) {
        lsnum = RLENGTH
        a[lsnum] = "." substr($0, RLENGTH + 1)
        p = 1
    }
    if (p == 1) {
        for (i in a) {
            printf "%s", a[i]
        }
        print ""
        lsnum = 0
        p = 0
    }
}

END {
    if (length(a) == 1) {
        print a[0]
    }
}' file
foo
foobar.bar
foobar.baz
foobar.baz.bat
bar

EDIT: here is the above script formatted by gawk -o- for readability:

{
        match($0, /^[ \t]*/)
        if (RLENGTH == 0) {
                if (NR > 1 && length(a) == 1) {
                        print a[0]
                }
                delete a
                a[0] = $0
                lsnum = RLENGTH
        }
        if (RLENGTH > lsnum) {
                lsnum = RLENGTH
                a[lsnum] = "." substr($0, RLENGTH + 1)
                p = 1
        }
        if (RLENGTH == lsnum && p == 1) {
                for (i in a) {
                        printf "%s", a[i]
                }
                print ""
                lsnum = 0
                p = 0
        }
}

END {
        if (NR > 1 && length(a) == 1) {
                print a[0]
        }
}