At the moment, if we have OAuth integration enabled with Bitbucket server/DC. The create branch option does not include the issuetype in redirect URL. This is the reason while creating a branch from Jira does not pref-ill the branch type in bitbucket. It only selects Custom branch type.

This same feature available from Application link does include issuetype.

• Create branch Redirect URL when creating a branch using the option available with Application Link.

   https://bitbucket-atlassian.com/branch/create?issueKey=TEST-3&issueType=Story&issueSummary=test 

• Create branch redirect URL OAuth:

•  https://bitbucket-atlassian.comcom/plugins/servlet/create-branch?issueKey=TEST-3&issueSummary=test