Could the old server have some local groups or accounts that inherited specific permissions for those files and folders and got lost during migration? You can check this by investigating current permissions for those affected folders and see if any unknown groups/accounts exist. You can use ICACLS for that purpose.
https://learn.microsoft.com/en-us/windows-server/administration/windows-commands/icacls.
If that is the case, you will have to rebuild/grant the permissions chain using domain-based accounts and groups.
You may consider using Storage Migration Service in the future to migrate your file servers and avoid those kinds of problems since it performs a complete audit of all the migrated data in terms of consistency and permissions, making sure everything works after migration.
https://learn.microsoft.com/en-us/windows-server/storage/storage-migration-service/overview
https://www.starwindsoftware.com/blog/migrate-your-file-servers-with-storage-migration-service