When you install Designer on a machine it does install the database and the Connect Server. It is just that without a license, your Designer will run like a demo.
Now if you check in your Windows Services, look for Connect MariaDB Server. is this running? If not, try to manually start it and check that the Connect Service is also running. Thoses are for the Connect server installed with your Designer on that workstation.
Now in order to still use the full capacity of your licensed Connect Server, you’ll need to go in your Designer->Window->Preferences->Servers->Connect Servers and there set the URL and username as defined on your licensed Connect Server.