Search Data is managed and created by search components in SharePoint.
You're unable to migrate the search data from a source environment to a destination environment.
The ShareGate migration tool currently does not support the migration of your search data. This includes the following:
- Crawled properties
- Metadata from crawled items
- Managed properties
- Search analytics
- Usage analytics
- Search index
- Search results
- Search configuration data
There is no solution or workaround at this time.