Do I still need my iTunes directory?
You are correct - both folders are not needed.

Once the new folder is set, you can consolidate all the media there, make one last backup of the old structure and delete it.

I’ve not seen them split often, so make sure you have a backup in case you find any old files didn’t migrate. Also, keep backing up - some people have felt that Apple Music was so good they stopped backing up only to learn months or years later that some tracks they wanted were substituted for ones close like non-explicit versions, etc.. The cloud isn’t your backup plan, it just makes it easier to sync. A cloud database also can get deleted or corrupted so test your backups from time to time.