Currently if you create an account on the web editor and log in, you will find the My Account > My Sketches view.
It looks like this URL is public even if you aren’t logged in – so there is currently no difference between a “public” and “private” sketch, if you know the URL. If there was going to be a general sketch search, it might need to give users control over what would show up in search results – and so need some concept of publishing / public sketches. You could look at things like Scratch, Codepen, etc. to get ideas.