I think this can be easily implemented with the Distill Web Monitor browser extension [1]. Just monitor the post listing page, set a CSS selector for the post titles, and add a text condition (e.g., "Awesome Blog Post Series").

From there, you can choose how often it checks and how you want to be notified (e.g., browser notification, email, etc.).

You can run it for free on your browser or pay for the cloud version.

[1] https://distill.io