Organizing and editing contact information within Microsoft Teams Free
It is not possible to add new contacts from the Settings -> People tab, but you can do this from the People app.
You can make use of the "Invite to Teams" option. Pressing this button creates the invitation link which you can send by email to the person you want to invite to Teams.
You can also search by the email, but this will only work if this email is enabled as searchable in this person's Teams account.