After validating that the issue is not caused by antivirus or firewalls between DSA and domain controllers, please make sure that configured service account in domain pair is having a full admin rights. This is especially important for the target domain, as this account should be able to modify multiple permissions and AD objects.
If more granular service account permissions need to be given, please consult this document:
Migration Manager for AD 8.15 - Granular Account Permissions (quest.com)
