use strict;
use warnings;

# @ID to keep unique id's (in order they are seen)
# %T to group things by id. Make it HoA (Hash of Arrays)
my (@ID, %T);
...

while (<HANR>) {
    my ($date, $id, $kw) = /\[(.+?)\]/g;
    my $txt;

    next unless $kw;
    $txt = "$+ to P5"  if $kw =~ /^(Input Message)/;
    $txt = $+          if $kw =~ /^(Orchestration Started)$/;
    $txt = $+          if $kw =~ /^ProcessName:(.*)/;
    # note the opportunity to merge some regexes above
    next unless $txt;

    push @ID, $id unless $T{$id};
    push @{ $T{$id} }, "$date,$id,$txt \n";
}

for my $group (@T{ @ID }) {             # this is a hash slice!
    print OUT for @$group;
}