Thanks! To be notified immediately, that would be the better way to go, you are correct.
I decided on JSON API solution because I’m not the admin of this Jenkins server and so not having to change the server (except of adding a view for the tests to be visualized) was a huge advantage.
At some point I have to keep track of “are jobs X and Y green?”
With MQTT that logic would be on OpenHAB side, because I only get updates.
With JSON API I just can fetch the result again, calculate what I need, and forget the rest.