Both are real pages on uni.xyz. uni.xyz itself is the community feed; the marketing homepage that used to sit at the root now lives at uni.xyz/about. The page at uni.xyz/new-home is a preview of a redesign of that /about homepage. It is publicly reachable, so a link to it works for anybody, but it is deliberately kept out of search results and it is not linked from anywhere in the navigation. Nobody arrives at it by accident.
Nothing about your account is different there
The preview sits on the same platform as the rest of the site. Your sign-in, your membership, your credits, your projects, your entries and your payments are identical on both, because there is only one account behind them. Nothing you do on one page has to be repeated on the other, and there is no separate trial or beta to join.
What it is for
It is a rebuild of the /about homepage being worked on in the open rather than behind a login. Its links go to the ordinary site: the competitions, the published work, and the pages about joining or hosting. Follow any of them and you are back in the site you already know.
Which link to share
Share uni.xyz/about. The preview is not indexed and its address is expected to change once the redesign goes live, so a link to it is not worth keeping. If somebody sent you one, nothing is wrong: the same starting points are all on the current /about homepage.
If it looks half-finished
It is. Parts of it are still being built, and that is not a fault with your account or your browser. There is nothing to fix at your end. Use uni.xyz.