Rafael,
I am no expert on this, but if you are using a server version, the tiddlywiki content is already accessible via the server, by definition. Jed has used a similar approach to make Bob wikis multi-access so it locks a tiddler at a time. So there exists a method to query the server already. Perhaps this would be your best approach first. ie investigate either bob server messages" or "native Node.JS".
If you use a single file wiki there are ways to import content from that wiki from elsewhere, but that's not what you are looking for.
My own interest in REST API's is the opposite, and comes from the fact that WordPress already has many API's, custom posts and more. I wonder if a TiddlyWiki could store all its tiddlers in the database behind WordPress in its database via REST API's, in part because such an internet service is easy to obtain. But Then WordPress could also access the tiddler content, a custom post type could even give access to a tiddler independently. We could programaticaly generate wordpress content from a TiddlyWiki.
Best of luck in your endeavours
Remember explaining what you want without a partial solution, may get you further when asking questions.
Perhaps you thought REST API's was the answer, but what was the question? You answered this in part, but the topic title may keep people away.
Regards
Tony