Eventually found a bug report from searching for the error messages in the thread tooltip.
https://issues.jenkins.io/browse/JENKINS-52374?page=com.atlassian.jira.plugin.system.issuetabpanels%3Aall-tabpanel
We were using Java 11.0.7, and the above issue mentioned a fix in Java 11.0.8. We upgraded to that, restarted Jenkins, and now no long see the Thread-xxxx in a waiting state.
Thread count has remained stable for 24 hours.