When migrating with ShareGate you must also migrate the hidden list “SPJS-DynamicFormsForSharePoint” – you must first make it visible by going to the Misc tab in one of your DFFS enabled forms in the old site. The same applies to the configuration for vLookups.
Please not that the hidden config lists must be migrated to the same site where your lists and libraries are migrated to.
When you now reinstall DFFS in the forms in the new site, it will automatically pick up the configuration for your forms.
Let me know if you have any questions.
Alexander