If a page in the client (e.g. enwiki) is connected to Wikidata and has *only* one site link (to enwiki), then it is not obvious at all to know that when on the client.
It has the "add links" link which is there if the page has no connection at all or the item is connected but has no other site links. (e.g. no "language links") When I see "add links", I might think to create a new item and not realise it's already connected.
It also links to the #sitelinks section of the item page which is great for editing site links, but not if you are interested in the statements.
To resolve this, we can put a link in the toolbox to the connected data item. We can also put something (e.g. wgWikibaseItemId) in the js config variables in the page so that gadgets and user scripts can do what they like with it.
bug 46229 and bug 48354