Another option for providing access is done at the Mailbox Level. This is very common in Shared Mailboxes. These are permissions that have been set by an Administrator, with many organizations using automation tools to control access. There can be several options selected.
These permissions can be viewed in the Admin Center UI and in PowerShell. However, collecting them, mapping them to the new system, and then applying them can be quite a pain. Again, we have you covered with our tenant to tenant migration service.