Thank you for the really fast answer!

This works:

use Plack::Builder;
use Plack::MIME;

for my $expr (
       ".c", ".cpp", ".css", ".csv", ".dat", ".dpl"
     , ".gp", ".h", ".hpp", ".html", ".ini"
     , ".java", ".js", "makefile", "Makefile", ".m", ".mac"
     , ".pl", ".pm", ".pod", ".py", "README", ".sch", ".sh", ".txt") {
  Plack::MIME->add_type($expr => 'text/plain');
} 
 
builder {
  enable 'Plack::Middleware::Static',
    path => qr{^/html/downloads/},
    root => '.'; 
      
  enable 'Plack::Middleware::Static',
    path => qr{^/html/(?!downloads).*\.(css|gif|jpg|js|pdf|png)$},
    root => '.',
    content_type => sub { Plack::MIME->mime_type($_[0]); }; 
    
  mount "/" => $app1;
  mount "/imggenerator.pl" => $app2;
};
[download]

Per default, Plack::Middleware::Static will serve your files depending on their extension by using Plack::MIME. So I suggest that you just drop your own invocation of Plack::MIME for the "normal" behaviour and override it for your download directory like this: content_type => sub { 'text/plain' }

Edited to add: After a glance at the code, you can also provide the content type directly:

content_type => 'text/plain'

Thank you very much! That does what I want and is clear to me:

use Plack::Builder;
use Plack::MIME;

my $expr = qr{\.c|\.cpp|\.csv|\.dat|\.dpl|\.gp|\.h|\.hpp|\.html|
              \.ini|\.java|\.js|makefile|\.m|\.mac|
              \.pl|\.pm|\.pod|\.py|readme|\.sch|\.sh|\.txt}xi;

builder {
  # normal behaviour outside of downloads
  enable 'Plack::Middleware::Static',
    path => qr{^/html/(?!downloads/)},
    root => '.';
    
  # plain text for non binary download files
  enable 'Plack::Middleware::Static',
    path => qr{^/html/downloads/.*($expr)$},
    root => '.',
    content_type => 'text/plain';
  
  # download only for the other download files
  enable 'Plack::Middleware::Static',
    path => qr{^/html/downloads/.*(?!$expr)$},
    root => '.',
    content_type => 'mime/type';
    
  mount "/" => $app1;
  mount "/imggenerator.pl" => $app2;
};
[download]

Have you confirmed that the server is actually sending Content-Type: text/plain? I know at least some browsers once would interpret text/plain as text/html if the contents "look like" HTML and I do not know if modern browsers still do that.

I believe that was only the pestilence known as Internet Explorer.