Please make the Bitbucket Server Integration plugin mark the primary branch of the repository with PrimaryInstanceMetadataAction (source, javadoc). That will allow other plugins to recognize the primary branch, e.g. in JENKINS-66689.

To implement this, the BitbucketSCMSource class (source) should override the SCMSource.retrieveActions(SCMHead head, SCMHeadEvent event, TaskListener listener) method (source, javadoc).

(The Bitbucket Branch Source plugin has this feature already; its BitbucketSCMSource class adds a PrimaryInstanceMetadataAction.)