I’d guess you need to change
builder {
mount "/plack" => $app;
};
to
builder {
mount "https://stackoverflow.com/" => $app;
};
because your alias is removing /plack/
or just change
# URL to be handled by FastCGI
Alias /plack/ /tmp/placktest.fcgi/
to
# URL to be handled by FastCGI
Alias /plack/ /tmp/placktest.fcgi/plack/
After all it does not appear to be a Perl question, but a System Administrator one, about Apache configuration.