For example, will abc.github.io/verbose/
(abc being my current username) be changed to xyz.github.io/verbose/
when I change my username to xyz? Will it be automated through GitHub actions?
When you attempt to change your username on GitHub, they explicitly mention that no redirects for GitHub Pages will be set up. Therefore, all links pointing to oldname.github.io/verbose/
will no longer work. It is even possible for someone else to register an account (or organisation) using your old username and then host their website there.
Here is a screenshot of the dialog: