pgAdmin doesn't create PostgreSQL servers, it provides a GUI to access and manage them, which is why you don't see a "create server" button - such a button existed in earlier versions but was poorly named.

Server groups are folders to organise your registered connections.

To add an existing server, right click your server group of choice, then "Register > Server...", and enter the connection details.

Some installations of pgAdmin may come bundled with a PostgreSQL server too, in which case you will have likely configured this server and set the credentials during installation. Alternatively, you may want to run your server through Docker, a VPS, or a managed Postgres hosting service, then register it in pgAdmin.