Depends on what you define "authority site" as. I don't think there's a magic line in the sand where you hit a certain metric or set of metrics and before you crossed that line you weren't an authority site and then tomorrow you pushed a little further and were.
As to your site specifically and whether 'I' consider it an authority site, it depends on what type of site it is. If its a niche product review site or something its probably not going to get any natural social traffic or very very few people naturally linking to it so its ok you don't have that, you do have a lot of content and decent traffic so it may be if that's what type of site and depending on the niche you're in. If its buzzworthy content, or entertainment or whatever though and you're not getting natural social shares, links, return visitors, etc. then I don't think I'd say its an authority site yet.
Another factor I look at is how does Google itself treat it? Do articles you put on your site natural rank at or near the top of Google for the keywords/phrases they're built around (losing only to other authority sites like news sites, brands you recognize, etc.)?
That's how I define an authority site. Something that is established to the point where new content is treated and ranked highly by Google naturally and you get natural links, traffic, social shares, etc. so your visitors/traffic and search engines are both treating it as an authority.
Some other people define an authority site simply as a non micro site/PBN site or basically any site they update regularly, continue to add content and links to and is their money site.
Basically, I dunno, you decide