Как я могу получить список всех файлов с определенным расширением из определенного каталога?

достаточно изменить одну строку:

my @files= map{s/\.[^.]+$//;$_}grep {/\.txt$/} readdir DIR;

If you can use the new features of Perl 5.10, this is how I would write it.

use strict;
use warnings;
use 5.10.1;
use autodie; # don't need to check the output of opendir now

my $dir = ".";

{
  opendir my($dirhandle), $dir;
  for( readdir $dirhandle ){ # sets $_
    when(-d $_ ){ next } # skip directories
    when(/^[.]/){ next } # skip dot-files

    when(/(.+)[.]txt$/){ say "text file: ", $1 }
    default{
      say "other file: ", $_;
    }
  }
  # $dirhandle is automatically closed here
}

Or if you have very large directories, you could use a while loop.

{
  opendir my($dirhandle), $dir;
  while( my $elem = readdir $dirhandle ){
    given( $elem ){ # sets $_
      when(-d $_ ){ next } # skip directories
      when(/^[.]/){ next } # skip dot-files

      when(/(.+)[.]txt$/){ say "text file: ", $1 }
      default{
        say "other file: ", $_;
      }
    }
  }
}

To get just the ".txt" files, you can use a file test operator (-f : regular file) and a regex.

my @files = grep { -f && /\.txt$/ } readdir $dir;

Otherwise, you can look for just text files, using perl's -T (ascii-text file test operator)

my @files = grep { -T } readdir $dir;

Просто используйте это:

my @files = map {-f && s{\.txt\z}{} ? $_ : ()} readdir DIR;