Is the server already in the files when I decide to export?

Do I have to do any extra things to release my game on lets say itch.io?

Yes, once the project leaves microStudio to live its own life, you will have to install your own server for it. The required steps are described in the documentation under Networking / Export ; microStudio lets you export your server app as a NodeJS app. You need to install and run this app on your own server.