Presuming you want to preserve the order and you won't have different interleaved (e.g. A A A B B B C C A B B, where keys seen before reoccur later) you just need to store off the current key's value.

my( $lastkey, @row );
while( <DATA> ) {
  chomp;

  next if /^\s*$/;

  my( $key, $datum ) = split /\s+=\s+/;
  if( $key ne $lastkey ) {
    print "$lastkey = ", join( ",", @row ), "\n" if @row;
    @row = ();
    $lastkey = $key;
  }
  push @row, $datum;
}

print "$lastkey = ", join( ",", @row ), "\n" if @row;
__END__
A = 1
A = 2
A = 3

B = 5
B = 1
B = 7

C = 8
C = 6
C = 7
C = 5
C = 3
C = 0
C = 9
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