Hi @DanieClaassen-8722,
In SharePoint Online, your storage space is determined by the plan you purchase. You can check how much storage space your plan has and the size of the content needed to be migrated. Then decide whether you need to purchase more storage. Please refer to this article for more information about the limitations and this article for information about adding storage.
As you are planning a migration, it is chance for you to reconsider your tenant architecture.
In fact, it is recommended that do not run multiple instances at a time when migrating is in process, and you can try to perform the pilot migration. This should use an incremental migration method, in which migration happens in the background with no user impact, followed by a cutover event in which SharePoint Server team sites are disabled and they are directed to use the SharePoint environment. This method is preferred as it reduces user impact.
If the tool you are using is SPMT, you can execute the plan according to the official document. If you are using a third-party tool, it is recommended that you seek guidance from the provider.
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