I tried to migrate a multibranch project from Bitbucket Branch Source Plugin to Bitbucket Server Integration. Before the migration, the Jenkins master read just the Jenkinsfile of each branch from Bitbucket Server over HTTP, and the Jenkins agent then cloned the repository and submodules and pulled Git LFS files. After the migration, the Jenkins master cloned all branches of the repository and pulled Git LFS files. We cannot afford to let the Jenkins master do that, because of time and disk space. I had to revert the migration for this project.
Please change the Bitbucket Server Integration plugin to support lightweight checkout for Jenkinsfile. Perhaps that is part of "SCM API 2.0" JENKINS-62002; I don't know.