I've been wondering about this too.

Let's say I finally released an Early-access version of my game(paid) after having a free demo-only page up for some time, what happens then? Will it get a boost in traffic? I couldn't really find any information about this on itch itself.

From what I can tell, Early access still counts as in-development, so does the system know that my game is now ready for sale? Is human curation by the itch.io team the only sure way of getting attention on itch? I've been thinking about releasing an itch only Early-access for my game, but the lack of details about how such things work really makes me uncertain.

Could any admin elaborate upon this? I'd really appreciate it. (and perhaps set-up a how-things-work guideline like Steam does?)

I recommend creating a devlog when you push out the update: https://itch.io/updates/devlogs-post-types-enhanced-browsing-and-more (see the A New System For Updated Games section).

A devlog "major update" post can boost how your page is ranked on our browse pages in terms of popularity. At the moment devlog posts are reviewed since we don't want people trying to abuse the system with low quality posts, so if you're posting an update post please put some effort into it. (Include text of changes, some images, any other information)