The idea is to create a website for my mother, without having to deal with hosting at all (static github pages).
Does this combination work that way?
Some static site generators have good support for generating pages from a dynamic source, say API, database or anything you can access using programming language.
See eleventy, for instance, has the “Javascript data files” [1], it run some JS code to generate a list of posts, here we can fetch from pocketbase, then, we can generate pages dynamically [2].
Pocketbase in this case just act as a lightweight CMS.
Is this what you’re talking about?
It is simple, so its single program is (1) a webserver, (2) runs server-side code, and (3) hosts a DB. I'm running a $12-per-month server on Vultr and its only service is PocketBase.
You don't need to host the webpages on PocketBase. If you wanted all your webpages to be on Github Pages, you could do that.
See my explanation on my reply to the original post.