Whether you purchased Age of Empires II: Definitive Edition on the Microsoft Store or Steam, you will be able to create and play multiplayer matches with each other regardless of your platform. All you need to do is create a multiplayer lobby for it to show up in the universal game lobby.
If, for some reason, you cannot see your friends’ lobbies, be sure to make sure you are on the same game build and crossplay is enabled from the Game tab. If the lobby still does not show up, follow the troubleshooting steps in this article: I cannot see any game lobbies. What's wrong?