Is it possible to search on MavenCentral (search.maven.org) by REST, so that I get the search results in JSON/XML (or some other machine readable format)?
Sure, open your Web Inspector/Developer Tools window and visit (e.g.) https://search.maven.org/artifact/org.mockito/mockito-core
Filter XHR requests and you will see which URLs to use and what the JSON response looks like.