Currently, in Bitbucket Server, it is not possible to import metadata such as Pull Requests History neither using the out of the box feature to import code from an existing project to a BB server instance nor using REST API.
Note: For Data Center, such a feature is provided via the Data Center Migration for Admins tool for Server TO Data Center or Data Center TO Data Center migrations.
Provide a tool that would import this metadata via UI.
provide a REST API endpoint.
For Bitbucket Cloud users, Bitbucket Server users, Gitlab users etc... who consider migrating data to a Bitbucket Server such a feature would be a great add to not loose Pull Requests history (for example).
Currently, a valid option would be to consider purchasing a Data Center license.