Devin Nusbaum unfortunately, I don't. I've got a few 1000+ LOC pipelines running continuously. I do not know how to tell which one leaves executors and when.

Pipeline build that has such "likelyStuck" executor looks completed on its build page (no progress bars, build status is set). But I still can see a matching OneOffExecutor on master:

      "_class" : "hudson.model.Hudson$MasterComputer",
      "oneOffExecutors" : [
        {
          "currentExecutable" : {
            "_class" : "org.jenkinsci.plugins.workflow.job.WorkflowRun",
            "building" : false,    // always false for these lost executors
            "result" : "SUCCESS",    // always set to some valid build status != null
            "url" : "JENKINS/job/PIPELINE/BUILD_NUMBER/"
          },
          "likelyStuck" : false    // can be true or false
        }, ...

Anna Tikhonova Are you able upload the build directory of the build matching the stuck executor? Specifically, it would be helpful to see build.xml and the xml file(s) in the workflow directory. EDIT: I see now that you can't easily tell which are stuck and which are good. If you can find an executor with likelyStuck: true, and whose build looks like it has otherwise completed or is suck, that would be a great candidate.

Another note: JENKINS-38381 will change the control flow here significantly.

gives you the jobs currently running

This is not really an appropriate API query to use for that question. If your interest is limited to all Pipeline builds, FlowExecutionList is likely to be more useful. If you are looking at builds of a particular job (Pipeline or not), I think that information is available from the endpoint for that job.

TCP prevents scheduling more builds because it considers those hanging executors.

Offhand this sounds like a flaw in TCB. This PR introduced that behavior, purportedly to support the build-flow plugin (a conceptual predecessor of Pipeline née Workflow). If TCB intends to throttle builds per se (rather than work done by those builds—typically node blocks for Pipeline), then there are more direct ways of doing this than counting Executor slots.

Offhand this sounds like a flaw in TCB.

I am attempting to fix this flaw in jenkinsci/throttle-concurrent-builds-plugin#57.