Please add a way to configure the Atlassian-maintained Bitbucket Server Integration plugin not to report any build status to Bitbucket Server.
This is similar to
JENKINS-49216 / JENKINS-49471 / JENKINS-36755 for Bitbucket Branch Source. There, the solution was to install Skip Notifications Trait Plugin and then add that trait to the branch sources. However, Bitbucket Server Integration does not seem to provide any withNotificationsDisabled method that Skip Notifications Trait could call. nor any other way to disable the notifications.