Here is the tour in the help center.
You can see that it refers to this site as "Academia Stack Exchange" (full name) and "Academia" (short name).
"Academia.SE" and "Academia.SX" are popular abbreviations for the full name ("Academia Stack Exchange").
There are various grammatical rules about using definite articles (like "the") before a proper noun (like "Academia"). We don't use "the" before the name of a website, book, movie, etc. Hence "the Academia" is wrong. It's a matter of English grammar, not an Academia-specific preference, policy or regulation.
You could argue for "the academia Stack Exchange" as a short way of saying "the Stack Exchange site about academia," but that would not apply to "the Academia." (And it would generally be strange to refer to this site that way while on this site. It makes more sense to use this if you're writing for an audience that might not know there is a Stack Exchange site about academia.) This would also not apply to "the academia website" (as a short form of "the website about academia"), because there is more than one website about academia - this would be an incorrect usage of "the."
"Academia website" is also wrong. "Academia" is the name of the website; in English we don't follow the name of a thing with the type of thing it is. (Unless the type of thing it is happens to be part of the name, like "Columbia University".. or "Academia Stack Exchange"!)