Hi Alex,
you could use the endpoint that JATOS' GUI is using: /jatos/status, but to make this work outside of a browser you have to deal with JATOS session cookies. But you can try it out in the browser (if you are logged in in JATOS in this browser): open a tab and go to my-jatos-domain/jatos/status. I can give you more information if you want to follow this path.
Newer versions of JATOS have an API that has an endpoint /jatos/api/v1/studies/properties, that would give you all study (and component and batch) properties of all studies where your user is a member of. But this is not available in 3.6.1 - only from 3.8.1 on.
Best,
Kristian