Of course, we should ensure that even our basic API tests are built to cover "Triple S" checks i.e. Status code, Schema, and Scenario checks but when we test our APIs, we should NOT just focus on the request and response part of our APIs but most importantly we should understand that how application(s) are going to consume our APIs. This will definitely give you a solid set of additional use cases from an end-user point of view to cover all your bases.
A blog about my testing stories where I pen down my thoughts about test automation covering primarily Selenium, Java, Rest Assured, Karate, Maven, TestNG, Postman, newman, Jenkins, Git, Azure DevOps, etc.