Edit: note the flaw pointed out by Hautex. I did not understand the question correctly, and did not check uniqueness of the correct title.

How about this loop?

foreach my $filename (sort keys %mycorpus) {
  my $titles = '';
  my $counter = 0;
    while ($mycorpus{$filename} =~ /title:#(.*?)#\s*$/gm){
      if($counter++){
        last if $counter++; # skip the rest of the matches
        # can also be used to print warnings about multiple titles
        # and check $1 against $titles if they are the same, or not
      }else{
        $titles = $1; # first match, we can store it,
        print  "$titles \n"; # or print it out
      }
      
  }
}
[download]

the output is

this is text I want 1 
this is text I want 2 
this is text I want 3
[download]

You can also replace the while with an if, and then it just matches the first title# .

foreach my $filename (sort keys %mycorpus) {
  my $titles = '';
    if ($mycorpus{$filename} =~ /title:#(.*?)#\s*$/m){
      $titles = $1;
      print  "$titles \n";    
  }
}
[download]

The output is the same. I think you wanted the multiline regexp modifier to match a newline inside your filedump string.

edit: better structure to allow more post-work (commented what can be done there). Did also remove the /g (go) modifier in the "if" example as it is not needed there.