I suggest providing a summary of the purpose of a StackExchange site up-front (i.e., near the top of the page).
Probably as a "Rounded/Squared Question Mark" button to the left of the site's logo, which upon click will pop up a box containing the site's description. Implemented this way, it won't become a clutter, and yet allow for a long-and-detailed description.
This feature will, IMO, help newcomers quickly find out what a certain SE Site is about.
(In fact, I'm not a newcomer (have been using SE for quite some time), yet when I landed on an SE Site I had to spelunk quite a bit to find out what exactly the site was about, to determine whether my question should be asked in that site or on another.)
Edit: After reading the question 'suggested' as duplicate of this I have to disagree. That question was specifically about new user. But this question is about a newcomer to an SE subsite, not necessarily a new SE user.
As I have explained in my endnote of the original question, *I* am not a new SE user, yet when I happened on a subsite that I have never visited before, say this one, I honestly have no idea what the site was about (i.e., what questions are welcome and what are not). And I have been a not-new-user for quite some time I forgot how to find info about the site.
I scroll dooooown, see "About Us", clicked... and off I went to a page about "The StackOverflow Company", not about the SE subsite. Only after clicking "Tour" did I find information to what a subsite is about. And that led me to a new page (or opens a new tab depending if I forgot to hold Ctrl or not).