Can't add single contact to MS teams

Hello

Correct, there's currently no supported way to add contact in Teams' people tab. This tab only syncs contacts from your Microsoft account and your mobile device's contacts. It is more of a feature to "present" you what's in your Microsoft account or mobile device's contact list.

So, you would have to add via those sources in order for them to show up in Teams.

I would suggest that you submit this as a feedback as well so the product team gets it. https://feedbackportal.microsoft.com/

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.