You can set the ShareType and Visibility values for files being migrated from the Source to the Destination org. Simply toggle the settings while using any of the migration options: Migrate Selected, Migrate All, or Migrate Via Batch. Please note that this option is only available for Files (ContentVersion).

PS: View Mass File Migrate Salesforce file migration app on Salesforce AppExchange:
https://appexchange.salesforce.com/appxListingDetail?listingId=e9874a66-2001-4e3d-8a29-3a2ed7f584c4