[JENKINS-75224] Remove support for ?jsonp parameter in JSON flavor

[daniel-beck]

JENKINS-75224

Testing done

mvn clean install -Dtest='ApiTest,UpdateCenterTest,DefaultCrumbIssuerTest' in core

Compared https://ci.jenkins.io/contextMenu?jsonp=callback (?jsonp supported) to http://localhost:8080/jenkins/contextMenu?jsonp=callback (?jsonp ignored, looks like JSON now).

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