I cant capacitate how your example can be similar to others in this thread where syntax like my $foo = $r->under('/foo')->to('foo#baz'); are presented like in the docs.

That code looks more like it comes from a regular Mojolicious application rather than a Mojolicious::Lite application - see Mojolicious::Guides::Growing for the link between the two. Basically, Mojolicious::Lite just adds some sugar to make accessing the API easier. For example, in a regular Mojo app, one might write my $foo = $app->routes->under('/foo')->to('foo#baz'); (which would call the sub baz in AppClass::Controller::Foo as the handler), while ::Lite just has the under helper to make that easier: it just calls the sub that you pass to it, and it is automatically applied to any following routes (or routes in the same group), whereas in the previous example one has to use $foo to define routes that are affected by the under.