In order for an API communication to be created in Salesforce, is there anything that needs to be created in addition to a ConnectedApp and a class with the annotation below?
You don't "need" a Connected App, unless you plan on using it for an authentication method. You don't necessarily need anything other than the class (e.g. if this is an internal "API" called in Salesforce). You might need a Community, a Site, or a Connected App depending on how you want to use this externally.