Template Toolkit is used almost exclusively for templating, although being Perl, there's lots of ways to do it (including Mason, which is a bit more PHP-esque).
DBIx::Class is the mature and most widely used DB interface, and seems to interface nicely with almost anything: https://metacpan.org/search?q=distribution:DBIx-Class+DBIx::...
All frameworks (ish) play nicely with Plack, which is a straight rip-off of Rack, but of course being Perl, there are a gazillion well-documented, well-tested, and sensibly installable plugins for it: https://metacpan.org/search?q=plack%3A%3Amiddleware
And then there's Moose, which provides a sane interface to the mind-boggling flexibility of the Perl object-system 'hack': https://metacpan.org/module/Moose
Programming in Perl on the web has never been as fun as it is today, and you'll find mst (who's a member here) was a lynchpin in most of the projects that made that true.
People talk about Perl being a glue language, and that's absolutely right: with CPAN, it's the ultimate mashup tool when you need it to be. It supports functional programming, Moose has made OO with it awesome, and it has a testing culture second to none.