> *** can not find package cairo >= 1.0.0
You need to have the underlying C libraries installed in order to use the Perl wrappers. Here is a good place to start:
https://www.gtk.org/docs/installations/windows
Note that if you really want/need to use Gtk2 rather than Gtk3, you need to change the corresponding lines in those instructions. For example:
pacman -S mingw-w64-x86_64-gtk3
becomes
pacman -S mingw-w64-x86_64-gtk2
Once you have installed Gtk itself, you should have more luck with the CPAN install.
As a side note: GTK2 is EOL since December 2020, and nobody should write new code using it.
GTK3 is in maintenance mode (no new API, no new features), and the current stable release of GTK is GTK 4.4.
Sadly, there are no Perl bindings for GTK 4 as of yet, though you can easily use Glib::Object::Introspection to load the introspection data, just like you'd do with GTK 3.