I have checked the project guidelines, and from what I've read, I'm assuming that creating a new project page for a completed free game, one which already has a demo up here, isn't breaking any rules - but I'd like to make sure.  I would also like to ask the community: is this a good idea or a bad idea?

I have a few personal reasons for wanting to start a new page - for one, I was initially a tad reluctant to release a demo (long story), meaning I kinda just dropped it here casually and without any real promotion.  Ratings, comments and such were not enabled for that release, so I don't think there is really anything that I'd lose from it if I created a new page.  Also, this was back in 2021, around when I had originally planned to release the game - though back then I wasn't planning on actually releasing it on this site.  I had plans to have it published, but it soon became apparent that wasn't going to work out, which in turn took a toll on my mental health, leading me to distance myself from any further sorts of promotion.  Two years later (and finally starting to feel better), it might now look like my project is dead after said lack of promotion and updates, when that couldn't be further from the truth.

So basically, I want a fresh start, I suppose one could say.  I'm aware that newly uploaded projects appear in a "most recent" list, which I feel could be beneficial to regaining any visibility I may have lost since uploading the old demo.  However, if that is either considered poor practice and/or etiquette, or something that would prevent my game from getting indexed, I'd like to know.  I'd also like to know if there are any benefits to just updating the old demo's page, if there are any in my position.

I am planning on releasing my game sometime early next year.  It will be completely free, no donations or anything.  Thank you for your time!

You shouldn't make too many project pages, as a general rule. You can have a demo on the same page as a completed game. And you should promote your game outside itch.io anyway, that helps more than showing up in New Releases for a few hours.

In your case I would recommend using the same page.

Typically, newly published pages get a boost in our ranking algorithm, so you may be tempted to create a new page to take advantage of this.

But, you can also be eligible for this boost by publishing a “Major Update” devlog and attaching files to it. (Assuming it’s been a significant amount of time since the page was initially published.)

A new page will cause confusion for those that may have added the existing page to a collection, waiting for a full release, which is why we typically do not recommend it.

Additionally, an established page will have a better “historical” score for our popularity ranking algorithm, compared to a brand new page. The views/downloads/etc. that you have accumulated do count for something. I made post outlining how some of our algorithms work here: https://itch.io/post/1276094

Hope that helps

for those that may have added the existing page to a collection, waiting for a full release

This.

I even lost games from collections, because developers did some creative shuffeling with their updates and "new" projects.

Thank you all for your replies, and for helping this (sort of) newbie out!  It sounds like updating the page is the way to go after all.  The bit about "major update" dev logs is especially good to know, along with the thing about collections (huh, it turns out I'm in quite a few).  All very, very good things to know.