If a user of Twitter adds a link to a WMF site to a tweet in Twitter, it shows up in Twitter as commons.wikimedia.org/wiki/...
The name of the linked article is often not shown.
Links to other websites are often displayed in Twitter as a box with an image, the title of the webpage and the name of the web site, which is much more likely to get clicked.
Probably image from wikipedia cannot be shown in Twitter for licence reasons, but WM could generate ersatz images for display in Twitter, possibly a text logo based on categories or the wikidata description. Then WM links in Twitter could show up with this image, the title of the article and the name of the wiki the link is directed to.