As far as I am aware, it is possible to do this by updating the whole item, i.e., GET/POST of the `config.xml`.

Yes, and until JENKINS-20208 is implemented, there is not going to be anything else.

It'd be great if it was officially documented.

Seems redundant. It's part of job configuration like everything else, so is configured through the job config.xml API like everything else. Otherwise, every plugin that contributes a build step similarly would need to explain how to use the job config.xml API. What am I missing?

Agree. The problem IMO, is discoverability. I don't remember how I learned that it can be done as I wrote in the description. So maybe it is worth just making a note that to update the matrix via API, use generic `/config.xml` API with a link to the doc about that API (if it exists on jenkins.io).

Right, my question is, what sets this apart from any other plugin adding some stuff to job config.xml files that can be edited through the normal POST config.xml API?

Unclear what the need for this is, given the plugin does nothing special and general API docs apply.