Thanks for the links and the context. At a really quick glimpse the ebook suggests that you host your own WordPress sites locally for testing purposes. From what I've read so far you have an existing WordPress site and are looking to programmatically query some of the associated data from time to time, using it to do something or other. If this is the case, unless you want to work through this whole book, hosting sites locally for test purposes I suggest this is overkill.
Without knowing how much you know I'll mention a few things. The WordPress docs I linked to explain how their REST interface should be used. If you have curl installed you can run their example code for followers (if you have provided authentication details matching their site, rather than the example they provide), and see the response it gives you.
You could scrape this via WWW::Mechanize::Chrome, however it's always better to use an API if one exists, less subject to change, fewer prerequisites, often more portable. So depending on exactly what you want to achieve perl offers lots of ways to solve the problem, including REST::Client, HTTP::Request::FromCurl (this live demo lets you convert a curl request to perl code) and so on.
Take a look, do some reading (Super Search is your friend), let us know if you have specific questions.