Hi @Benton, Steven
You don't need to manually transfer contacts from Classic teams to People App in New Teams.
You can view contacts directly from All contacts in People App.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.