What does this look like in practice? Does Perl have a similar control flow syntax to awk?
It actually does (to an extent). There are BEGIN and END blocks (not used that much in regular scripting but they exist). There are also a bunch of perl command flags that can make things more awk-ish or sed-ish.
This random blog post gives something of the flavor.
https://lifecs.likai.org/2008/10/using-perl-like-awk-and-sed...
There's one fairly obvious error in that article: the fields are $F[0] etc, not @F[0]. Otherwise yes, that's a good way to make Perl look like awk. I personally translate awk concepts to more idiomatic Perl (I had no idea about -MEnglish, for example) but the concepts are still the same.
(That said, I do still have the tabs of perldata, perlobj, perlmod, and perlop open because I want to learn it better.)