There is an option in the advanced tab in connection manager to define a MySQL init-command for a connection. You can specify the database name in init-command option. That will be a default database for the connection. Please find the screenshot attached.
That does work for setting the initial database, but it doesn't select the database in the list of databases near the top of the window, which still reads “No database selected”. I will use this as a workaround for now, but I think it would be better to have an explicit option for this.