From the looks of it:

(namely, ".wikipedia.org" line) it seems that the tool can only work for Wikipedias. Based on https://commons.wikimedia.org/wiki/Special:Whatlinkshere/Template:Talkquote though I see that other projects are indeed supported, but seemingly only those that end with wiki_p (see the database names). So, commons.wikimedia.org is supported and some other wikimedia.org subdomains, but not Wiktionary and others.

Why is that? Are there difficulties with adding support for other databases?

In any case, it should be made clear that at least commons.wikimedia.org, meta.wikimedia.org, and some other domains are supported.

(P.S. The fact that there is no tag for the tool, instead of the generic Tools tag, means that I can't search for existing tasks that ask for the same.)