Teams doesn't have a contact list or address book. It uses the Chat feature to add people so you can talk, call, or arrange meetings with them.
The only why I have found to add contacts to Teams chat when using a personal Microsoft 365 license (Not work related), is to add their email address to the search bar at the very top of the Teams app:
When you type in their email address, it will then provide a name in the search results,
Click on it and it will then create a chat window and send them an invite to Teams.
Or if you want to add multiple people, click on the search bar and then click "Invite people to Teams":
It will then give you a link you can email out to your contacts so they can add Teams there side for you to contact them.
If they have Teams, it will just add you to their chat list and them to your chat list.
Teams chat, calls, and meetings, only work if the other person has access to Teams, be it via the App or Web Browser. They will need Teams there end.