Dear Christine Malan,
Thanks for reaching out to us here in Microsoft Community.
The date format for birthdays in the Contacts in New Outlook is determined by the language setting and cannot be changed.
This MM/DD/YYY date format is set by default because it conforms to the usage habits of users in the en-us, a.k.a. north American region and cannot be changed if your language is set as English (United States). If you switch your language to a different country that prefers the YYYY-MM-DD format, the birthday format will automatically change.
I am sorry this customization option is not introduced in New Outlook. If you want to share this issue with the development team, you can choose Feedback from the Help tab of the Outlook ribbon to report this problem or click this link Outlook · Community
You can stay tuned for Microsoft to be informed when this new feature is introduced in the future.
Best Wishes,
Stan - MSFT | Microsoft Community Support Specialist