Hello, @Sebastian Buus Jensen,
Welcome to the Microsoft Q&A platform!
After my test, the Get-RecoverableItems command is available in ExchangeOnlineManagement. If you could not use it in this module, there may be some mistakes during your using process. For example, make sure you have Connect-ExchangeOnine before using the command. Below are my test results for your reference:
If you still encounter error when using command Get-RecoverableItems, you need to check whether the version of your Windows PowerShell is the newest and if you have correct permissons to run this command. According to the official document, this command is available only in the Mailbox import Export role and by default, the role is not assigned to any role groups.
Should you need more help on this, you can feel free to post back.
If the answer is helpful, please click on “Accept answer” as it could help other members of the Microsoft Q&A community who have similar questions and are looking for solutions.
Thank you for your support and understanding.
Best Wishes,
Alex Zhang