...
This case does not differ significantly from the process described in Bitbucket Server to Data Center (in-place). Once you migrate from one instance to another, all hook settings are also migrated. You only need to update the Pages for Bitbucket license when migrating to a different instance type.
...
To migrate specific projects or repositories, we recommend cleaning up Bitbucket first by removing any unwanted projects or repos and using the standard Bitbucket front-end (or the Bitbucket REST API for teams that are comfortable scripting). Once Bitbucket server has only the projects and repositories you want, use a standard Bitbucket migration process to migrate the Bitbucket data. This is the safest and most straightforward migration approach when to combining migration and cleanup tasks.
...
If you are interested in a cloud version, contact us and let us know!