Currently, the Jenkins API for jobs returns run parameter definitions in the following way (JSON here but the result for XML is equivalent):
Unfortunately this parameter definition does not include the build filter that can be set up alongside the projectName and description when configuring the run parameter.
I believe that including this filter in the JSON would be beneficial for some use cases while not affecting others. The proposed return value would look like this:
I would be very glad to implement this change myself if the change is agreed upon.
Furthermore, I would be interested in knowing whether there are any ways to circumvent the current behaviour and retrieve the filter nonetheless.