Upgrading to Datadog-plugin version 2.60.1 requires the workflow-job plugin to be at least at 2.40 

After this we witness Jenkins in a zombie state of not able to run builds i.e. via BuildNow, Time triggered, web-hooks. Also to note existing jobs after a graceful restart is stuck and do not continue.
We see multiple of these in our logs, which is similar to JENKINS-52362 , however rolling back to Datadog-plugin version 1.1 and using workflow-job 2.37 does not create the issue anymore.

//INFO: Running CpsFlowExecution[Owner[job/branch/build_number]] unresponsive for 3 min 30 sec
org.jenkinsci.plugins.workflow.support.concurrent.Timeout lambda$ping$0