Currently, the only available option to migrate the repository issue tracker to Jira Cloud is using the Jira export tool. - https://support.atlassian.com/bitbucket-cloud/docs/export-or-import-issue-data/
Unfortunately, it is not accurately migrating the issue tracker and there's no option to customize the migration.

Enhancement request:
It would be helpful to be able to have a way of migrating the issue tracker manually to Jira Cloud via a migration script.