When you move your project from “In Development” to “Released” make sure to make a new Devlog marked as “Major Update or Launch”, this will flag your project to be reviewed by an admin, and if it’s indeed a major update or launch, will be placed on similar lists like when it was first created.
Or, should I add a new page for the full (non-demo) version of my game?
That is definitely a bad idea, especially if you are doing it intentionally to gain more traffic. Can’t remember off the top of my head if it’s explicitly against the rules, but it sounds very dodgy.
The intended path is the one with the Devlog described above, you can still include a demo (assuming your project is paid) on the same page.
Hope this makes sense :)