Dear GLV,
Thanks for posting in the Microsoft Community
Based on your post, I checked alongside us and found the same result as yours. Even checked with multiple test tenants and found the same result. It seems that, at this moment, Contact list feature isn't available in New Teams.
New Teams is still under development and it is suggest sending this feature to the Teams development team by go to Help > Suggest a feature. Feedback submitted in this way reaches the product team directly, and they can add future updates. On this point, cooperation and understanding will be greatly appreciated.
Further move back to classic Teams, please go to More Option (...) > Turn off New Teams.
Screenshot for Turn off New Teams and Suggest feature option.

Thank you for your previous time. Stay safe and healthy.
Best regards
Ankita Vaidya