To stop Bitbucket Cloud from automatically assigning specific user groups to new private repositories, go to Workspace settings > User groups. Identify the user groups that are currently being automatically added to new repositories, click the group name, select Edit, and set Default repository access to None.

Note: The "Automatically assign new repository permission" setting is deprecated, and setting access to None effectively disables it, as per Atlassian’s documentation on legacy permissions deprecatio.